What would it need to make Greek the primary language of Christianity? Comparable to Arabic for Islam.
I think you'd have to have Rome not be the power centre of the times. That's why the Bishop of Rome became the Pope. You'll probably want to look up the various councils like Nicaea, Ephesus, and Chalcedon to see what the geographical splits were and who had political power next after the Bishop of Rome. https://en.wikipedia.org/wiki/Pope#History