You need a 19th century PoD, assuming the rest of the world/history is largely unchanged. The reason is since the 20s (if ever in Cyprus go to the memorial/museum at St. George's near Paphos, there's some interesting pictures on the wall) Greek Cypriots have been agitating to join with Greece. If there's any kind post-WW2 resistance to British rule, the British simply won't stick around in the long-run
One solution is when the British occupy the island in 1878, they decide to open schools (as they did), and that the schools should teach in English rather than Greek (this actual decision went the other way - it was down to one English guy, I forget his name, who choose Greek because he was classicist). The Greek Cypriots instead of regarding themselves as Greek, then somehow come to regard themselves as British subjects of the Greek Orthodox faith.
Another solution, perhaps combined with the first, is to mess up some of ther early Enossis (unions with the motherland) that developed the modern Greek state - perhaps there are even multiple Greek statelets. That way, the idea of joining the Greek motherland doesn't come up, or is simply disregarded as a wild-dream, as far as Cyprus is concerned. See
http://en.wikipedia.org/wiki/File:Greekhistory.GIF - what I'm talking about is the Greek state not getting the Ionian Islands, Aegean Islands, Dodecanese, etc.
Also, stopping the population transfers between Greece and Turkey in the 20s might help - if the Greek state is a mixture of Christian and Muslim, and the Turkish state is also the same type of mixture, then Greek/Turkish Cypriots won't regard themselves as aligned with one or the other by virtue of themselves being Christian or Muslim.