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From the same universe as the NI PMs list:

List of Irish 'Presidents of the Executive Council' (until 1939) then Taoiseach

1922-1938: W. T. Cosgrave (Cumann na nGaedheal)
1923 (Minority; support from Labour & Businessman's): Eamon de Valera (Republican), Denis Gorey (Farmers'), Thomas Johnson (Labour), Michael Hennessy (Businessman's)
1927 (Minority): Eamon de Valera (Fianna Fáil), Thomas Johnson (Labour), Michael Heffernan (Farmers'), William Redmond (National League Party) [1]
1932: Frank MacDermot (National Centre League Party), vacant (Fianna Fáil), Thomas J. O'Connell (Labour), Michael Heffernan (Farmers') [2]
1936 (Minority; Confidence & Supply with NCLP & Labour): Seán Lemass (Fianna Fáil), Frank MacDermot (National Centre League Party), Thomas J. O'Connell (Labour) [3]
1938-1939: Eoin O'Duffy (Cumann na nGaedheal) [4]
1939-1946: Seán Lemass (Fianna Fáil)
1939: Frank MacDermot (National Centre League Party), Eoin O'Duffy (Cumann na nGaedheal), Thomas J. O'Connell (Labour) [5]
1942: Frank MacDermot (National Centre League Party), Eoin O'Duffy (Cumann na nGaedheal), Thomas J. O'Connell (Labour) [6]
1944 (Minority; support from Independent TDs): Richard Mulcahy (Cumann na nGaedheal), Frank MacDermot (National Centre League Party), William Norton (Labour) [7]
1945-1958: Richard Mulcahy (Cumann na nGaedheal)
1945 (Minority; Coalition with NCLP & Labour): Seán Lemass (Fianna Fáil), Frank MacDermot (National Centre League Party), Oliver J. Flanagan (Monetary Reform-O'Duffite), William Norton (Labour) [8]
1949 (Coalition with NCLP): Seán Lemass (Fianna Fáil), Frank MacDermot (National Centre League Party), Oliver J. Flanagan (Monetary Reform-O'Duffite), William Norton (Labour) [9]
1953 (Coalition with NCLP): Seán Lemass (Fianna Fáil), Frank MacDermot (National Centre League Party), Oliver J. Flanagan (Monetary Reform-O'Duffite), William Norton (Labour) [10]
1957 (Coalition with NCLP; Confidence & Supply with Labour): Cearbhall Ó Dálaigh (Fianna Fáil), Oliver J. Flanagan (Monetary Reform-O'Duffite), Frank MacDermot (National Centre League Party), William Norton (Labour) [11]
1958-1961: James Dillon (Cumann na nGaedheal) [12]
1961-1970: Oliver J. Flanagan (Fianna Fáil) [13]
1961: James Dillon (Cumann na nGaedheal), Frank MacDermot (National Centre League Party), Brendan Corish (Labour) [12]
1965: James Dillon (Cumann na nGaedheal), Frank MacDermot (National Centre League Party), Brendan Corish (Labour) [14]
1969 (Minority; support from Independent TDs): James Dillon (Cumann na nGaedheal), Frank MacDermot (National Centre League Party), Brendan Corish (Labour) [15]
1970-????: Liam Cosgrave (An Páirtí Náisiúnta) [16]
1970 (Minority; Coalition with Labour; support from Independent TDs): Oliver J. Flanagan (Fianna Fáil), Conor Cruise O'Brien (Labour), Tomás Mac Giolla (Republican Sinn Fein), Seán D. Christian Democrat Dublin Bay Rockall Loftus (Christian Democratic Movement) [16]

[1]: CnnG performs better than expected and manages to form a Government once again with Labour and National League support.
[2]: The quiet campaign of 1932 was thrown into disarray with the assassination of Eamon de Valera by a Blueshirt (the effective paramilitary wing of CnnG). As a result the now leaderless Fianna Fail fell into infighting among potential leadership contenders and saw any sort of sympathy vote evaporate. As a result the fiscally conservative and pro-British/ Unionist rapprochement National Centre League Party (A merger between the National League and National Centre Parties) came second to Cosgrave's CnnG.
[3]: Sean Lemass was elected Fianna Fail leader in late 1932 and set about restoring the party's electoral fortunes. He was less anti-British than his predecessor and tried to look cordial with Belfast (as a result Lord Craigavon, the Northern Irish Prime Minister called a snap election - which he once again won resoundingly; ) he however railed against Cosgrave's Government's seeming happiness to support Britain in the event of a war with Germany and his treaty with Britain - which solidified British control over Northern Ireland the Treaty Ports. As a result of this Lemass managed to weaken CnnG support and very nearly won a plurality of seats and votes over Cosgrave.
[4]: Cosgrave opted to retire in 1938 after nearly two decades in power and after suffering a mild stroke the year prior. He was replaced not by his preferred successor Richard Mulcahy - but by Blueshirt leader and Interior Minister Eoin O'Duffy. O'Duffy was famous - or rather infamous for the crack down on anti-Treaty forces during the Civil War and the subsequent years - there were also allegations that it was he who ordered de Valera's assassination. O'Duffy was staunchly anti-communist and also had shown his fascistic leanings with his trip to the German consulate when he became President of the Executive Council. This was very popular with the Blueshirts and parts of the CnnG grassroots - less so with everyone else.
[5]: O'Duffy subsequently lost the 1939 General Election in a landslide to Lemass and his rejuvenated Fianna Fail which argued for "a return to normalcy." The NCLP once again became the Official Opposition in the Dail.
[6]: The 1942 General Election was effectively called on a single issue - that of reform the constitution of Irish Free State in order to remove certain reference to the UK (the Privy Council for instance.) It was also called in order to see if there was support for Lemass' neutral position on the war (it was in reality far from neutral - British troops could freely move and use the Treaty Ports in the IFS.) In the end the Irish people seemed to endorse this giving Lemass a slightly reduced majority. CnnG, once again led by O'Duffy failed to perform better than 3 years before and were seen to be in danger of being permanent replaced by the NCLP.
[7]: In the end the referendum failed by a 55-45 margin and Lemass' Government were seen to be rather incompetent in standing up to the UK and Germany when they violated Irish territorial waters. There was also the issue with German spies being caught in the IFS - who turned out to have been based there for several years. The 'scandal' coupled with Mulcahy's removal of O'Duffy as the CnnG leader and O'Duffy's subsequent sulking off with several supporters to become Independents saw FF barely maintain power against the rejuvenated CnnG.
[8]: Lemass was forced back to the electorate in early 1945 due to his Govt. budget being voted down and thus the Dail losing confidence in his Government. Mulcahy rose to power with Labour and NCLP support. Meanwhile the O'Duffyites managed to take more than 10% of the vote with the new Monetary Reform Party - led by Oliver J. Flanagan, a noted anti-semite and popular TD from Laois-Offaly (O'Duffy was deemed too toxic to lead the party - but was seen as the 'puppet master' of the party leadership - reigning from his position as Party Chairman.)
[9]: Mulcahy, while not seen as a necessarily charismatic individual was seen as a competent operator with a militaristic eye for detail over his coalition government. By 1949 the country had seen a gradual increase in industrialisation in and around what was formerly the 'Pale' area around (and including) Dublin. Generous grants and aid for farmers saw many gain
new equipment which was up to scratch with the equipment and machinery used north of the border in Northern Ireland. By 1949 the government was generally popular and saw a moderate, though adequate swing in their favour which was enough to increase its numerical majority well above that of Fianna Fail and the O'Duffites. Mulcahy announced that he would be forming a coalition with the NCLP in effect ensuring that the two parties would continue to move closer together; talk of a merger began to be made in the press, though MacDermot was quick to shoot down such suggestions.
[10]: The government maintained its policies from the prior Dail sitting and began to impose more economically liberal reforms to the country's generally paternalistic economic system. Fianna Fail and the social credit orientated O'Duffites, led by the charismatic Oliver Flanagan, protested the removal of price and wage controls, in a move which was called "fiscal self masochism" by FF leader Sean Lemass. The Irish public didn't seem to agree and handed the government a slightly increased majority - in effect ensuring that Lemass after his fourth election defeat, would have to go.
[11]: Fianna Fail made a surprising choice with the selection of former Attorney General Cearbhall Ó Dálaigh (or Carroll O'Daly as he would refer to himself) as party leader. A generally moderate individual who was held in high esteem by members of all sides of the Dail, O Dalaigh was a highly effect speaker who had been considered for a top legal position within the nation. He was an able figure to criticise the government's economic policy, he was also able to answer the government's (usually rhetorical) questions of 'what would you do then?' He responded with a 'Contract for the Irish People,' released along with their hypothetical coalition partners the O'Duffites, which argued for a greater public works programme, various welfare programs, and lower taxes for middle-to-lower income individuals. These policies were popular outside of the NCLP's business supporters, and is seen to be a contributing factor in Fianna Fail's near victory in 1957 - which forced Mulcahy to, along with his NCLP coalition partner, gain the support of the Labour Party for day to day running of the country.
[12]: Mulcahy was well into his seventies when he decided to stand down as Taoiseach. He was replaced by External Affairs Minister James Dillon, who was the son of former IPP leader John Dillon, who had presided over the party's collapse at the 1918 general election. Dillon was a colourful contributor to Dáil proceedings and was noted for his high standard of oratory. Compared to Mulcahy's tenure as Taoiseach, Dillon was relative hands off, letting his ministers 'run free.' This saw attempts by the NCLP Finance Minister to try and get rid of the already rigid welfare system. This was unpopular and saw the government's popularity fall after the brief upswing when Dillon became Taoiseach. Nobody bar the strong CnnG supporters was shocked when a majority Fianna Fail government was formed in 1961.
[13]: They were shocked when Oliver Flanagan was the man to take the post of Taoiseach. Flanagan had overseen a merger between his party and Fianna Fail in 1959, under O Dalaigh's leadership. O Dalaigh's death in a car accident in 1960 paved the way for his surprise victory over Jack Lynch to become the leader of the new unified party. Flanagan had emerged on the political scene in 1942 when he became an Independent TD for Laois-Offaly. In his maiden speech he stated that the government should "rout the Jews out of this country." He was also a virulent social conservative, once famously proclaiming that "there was no sex in Ireland before television." Nonetheless his values, attention to listen to his constituents' concerns, charisma, and his ability to be one of the cutest of cute hoors in the Dail.
[14]: The implementation of the 'Contract for the Irish People' was immensely popular and made Flanagan's re-election a virtual certainty. This however did not highlight the fact that FF had little to no allies in the Dail, made even worse by the abrasiveness of Flanagan. The threat of a cross party anti-FF coalition was still prevalent. Though Fianna Fail was able to celebrate their second majority government in four years.
[15]: What a difference four years can make, the country's economy hit a road bump in 1967 and Flanagan's increasingly authoritarian and clerical-aligned government was starting to lose steam. The fact that it appeared to be running out of ideas for legislation by 1969 ensured that the government was called a 'zombie government.' While at the ballot box the government came only four seats short of a majority, the anti-FF parties hand nearly enough seats for a majority. Flanagan, proving his ability as a political Houdini managed to gain the support of a handful of Independent Dail TDs, ensruing his government would survive for the meantime. Though many thought that that the FF government wouldn't last in the long term.
[16]: These voices were ultimately proven right when Flanagan was forced to call another election after realising that his government was untenable in its current form. While Fianna Fail fell a mere 5 seats, the hypothetical coalition of the united party of CnnG and NCLP - The National Party (or An Páirtí Náisiúnta) now led by former CnnG External Affairs Minister Liam Cosgrave, who was the son of former President of the Executive Council, W. T. Cosgrave. Cosgrave was similar to Flanagan in his social conservatism (having been a strong opponent of liberalising contraception laws), but without the 'nasty bits.' Cosgrave however was seen as rather bombastic, at one stage attacking 'welfare blow ins' - something Flanagan capitalised upon. While Fianna Fail made some headway over the course of the election and would once again come tantalisingly close to majority (with their Independent allies forming a technical group called the Christian Democratic Movement.) The 'National Coalition' of APN and Labour would however scrape home with support from Independent TDs. The rise of the militant Republican Sinn Fein party, with links to the border campaign in the 1950s drew some concern on both sides of the border, but they were written off as a bunch of 'blow outs' (to quote Cosgrave out of context) or "bums" (to quote Flanagan, who would remain leader of FF.)