Ok I'll copy myself from an earlier thread.
Lets begin with the Greek parliamenary election of 1933 and George Kondylis reconciling with Venizelos. This shifts about 4.2% of the vote from the royalists to the republicans, just enough to turn a close victory of the former to easy victory of the latter. This has certain positive effects for Greece. The country avoids the instability of 1933-36 which almost led to civil war and did bring restoration and a royal dictactorship under Metaxas. Come 1940 it is still a republic and thanks to having 3 more years preparing and avoiding the purges of republican officers is militarily notably stronger and less internally divided. When Mussolini attacks the Greeks mobilize 600,000 men instead of 450,000 and push back the Italians even harder than OTL. When the Germans intervene the Greeks with more troops to start with and without Papagos in command have shifted significant troops on the Olympus line. The Germans still win but it's slower and harder. By the end of it the allies are still holding Crete and the Eastern Aegean islands while tens of thousands of Greek troops have escaped from the mainland along the British.
Fast forward to 1946. Greece had a relatively better war. No civil war between the resistance organizations, thanks to the continuation of the republic in 1935 and the Greek government in Crete. EAM is still signficant but republican organisations were even more so. And the Greek army in exile has gained a lot of PR from fighting in North Africa and Italy. Without the civil war as an excuse the Foreign Office proposal for union of Cyprus with Greece takes place in 1946. Before that turns a major issue in the 1950s. By 1952 when both Greece and Turkey join NATO they are friendly to each other, have a fair bit more goodwill, the East Aegean islands were being supplied through Anatolia during the war, and Cyprus has ceased being a problem before even occuring.
It goes uphill from there. The September pogroms against the Constantinopolitan Greeks never happen and Greco-Turkish relations keep improving with every passing year, with increasing trade and investment between the two countries and a common enemy in the Soviet Union and her satellites. The Turkish army without Cyprus and tension with Greece is relativey less influential within the country. Greece joins EEC in 1973, backing Turkish entry afterwards (similar to what the two countries had done when they tried to join NATO) and by 1980 there is a free trade agreement betwen Greece and Turkey and joint arms procurement and production. By the turn of the new century Greece and Turkey are no different than France and Germany. Talks for a loose federation within the EU which Turkey joined in 2004 are underway though not expected to end anytime soon...