IOTL they are under the American's nuclear umbrella, so the issue is to either remove that umbrella or make some series of Turkish governments consider they need an independent nuclear deterrence.
Things that come into my mind:
*Avoid cold war altogether. Hard with a 1945 POD, though. Under such an ATL, the Turks might still want a nuclear deterrence against the USSR
*An unfriendly regional power gets nuclear weapons and the Turks don't trust the Americans to protect them against that country. The obvious choice is Israel, and having Turkey involved in the many wars in the middle east is likely to do the trick. Israel, OTOH, wouldn't bomb Turkey's nuclear research facilities as they did with the Iraqis and Syrian ones. Then again, with a 1945 POD, other countries can remain aligned with the USA and, yet, unfriendly with Turkey.