What would happen if some time in the 60's the Irish elected Taoiseach Crazy McLooney who recognising that Ireland would get squashed flatter than a pancake in a military confrontation over Ulster decides the solution is to build up the Irish Defence Force until it can capture the North and implement a full North Korea style program of militarisation; i.e. 20% of the population in arms, 50% of the economy devoted to military needs etc. Bob the Alien Space Bat decides this is hilarious and works his magic and the Irish people go along with this and the rest of the world, including Britain neither notices or reacts. In addition the Irish economy stays at the OTL level despite a drastic drop in living standards due to the military build up diverting resources.
Under those circumstances could Ireland build a military force capable of taking and holding Ulster against Britain, NATO cannot intervene and nuclear weapons are banned.
It's still a huge ask given the situation that OTL Ireland was at by 1960's
OK, 1961 the Irish population was 2.82 million (the lowest since the famine) reaching 2.9 million in 1970 (which means at a rough guess the NI population alone is near half the ROI population), so that's a maximum of 540K based on your 20% population in 1960, reaching 580K in 1970
Looking at some GDP figures I've found Irelands GDP was 1.6 Billion Dollars in 1960 reaching 3.4 Billion Dollars in 1968, that doesn't leave you with much room to play with even with 50% devoted to military purchases.
Given that Ireland would need to field at least some form of Navy and Airforce as a combat force, and starting with nothing it would be a huge capital expense. The Navy "could" be built in Cork but would have to be foreign import designs, electronics, weapons etc. The Air Crops would all be foreign as well so that's a huge drain on foreign reserves.
The Army's maximum training exercise was 2 divisions during WW2 so the gaps of training such a force would also be huge. Like I said no modern Armour, Artillery, Anti-Tank systems, barely switched over to NATO standard for PDF, still .303 for Reserves. No large scale training for integrated operations.
Hell you are talking about the largest Government building plan just to house these new forces, with new Barracks, Naval Bases, Airbases. All built to "modern" designs, (again something that really hasn't happened ever, with only the legacy bases being modified for uses)
It's too big an ask and given the naturally larger strength of the UK and Institutional Experience of the British Forces I don't see it turning out well. And even if the UK doesn't notice and even if operations go well, at this time the Punt is tied to the Pound (and exports are still predominately to the UK preEEC) so Day 1 the Irish economy free falls in every way imaginable.