This was exactly the system that was used in EUIII (introduced after a few patches to replace the system I mentioned earlier) in fact. A missionary would sit in a province and would have a yearly chance at converting it. In theory the missionary could sit there until the end of the game. But it usually took somewhere between five and twenty years to do.
The EU3 way cumbersome with sending in new missionaries everytime you got one, hoping that he would luck on that 3% chance half a year later.. much like the colonization.
Maybe looking at the EU4 colonist gives a better solution: A missionary founds a 'religious colony' that grows over time while he is present.
Events and modifiers then can affect this growth and progress.
Higher basetax/ conversion resistance is like harsh climate, slowing down conversion.
Missionaries in higher basetax provinces should then be more expensive, too.
When the 'colony' is finished, the province will be converted.
This would work better with nonbinary religions makeup of provinces, though (i.e. province may be 50% Catholic, 40%Protestant, 10%Reformed, not just Catholic). Then, the missionary shifts around these values. And they may slowly change by themselves, too - like a tendency to become a monoreligious province (dominant religion grows slightly faster), bonus to state religion (slight increase) and Europe-wide bonus during reformation for Protestant/Reformed.
Tolerance and tolerance effects could then be calculated as the average tolerance weighted by prevalence.
