So, Islam had a fantastic policy for converting Christians, Jews, Zoroastrians, etc. to their faith. The Jizya tax being one example, and the fact that it was STILL often lower than what they were paying before anyway while nevertheless offering a financial incentive to convert.
So, my question. How could a medieval Christian nation that has conquered a large Muslim population encourage them - without violence - to gradually convert over the centuries. Presuming they were willing to go completely against the typical methods of their brethren, that is.
Either Orthodox or Catholic would work, though, really, it would probably be the former rather than the latter.