I disagree with the previous posters. In my experience, a well-placed high-ranked assassin can solve all of your Pope problems. I did not waste time and money building churches and training priests, because I have so far killed 5 or 6 Popes in a row with a single master assassin (rank 7 or 8/10), who is not even my highest-ranked assassin. Another master assassin killed the Pope while he was on expedition in Morocco. I think you might be interested to know that I have several master assassins at my disposal, the highest-ranked of which was a 9/10. But all you need is one, like the one I have permanently camped outside of Rome, with a high chance of success against the Pope (74% in my case) to remove him as soon as he is elected. My chance of success was good enough that I did not need to try more than once for every assassination. I have killed so many Popes and cardinals that there is no one left in the College of Cardinals to elected a new Pope. So the game has had no Pope for several turns now because the priests from the remaining Christian factions are all rookies who are far from being promoted to Cardinal. Although I did not need to try more than once each time against the Pope, you can ensure success as long as your assassin has a >50% chance of killing the Pope. Just save the game prior to the mission, so that If your assassin fails the first time, load the game at the save point and he will succeed in the second try.

How did I achieve the assassination Hall of Fame? Well, in addition to training a lot of assassins early in the game, I made sure that every assassin performed a mission every turn. I had so many successful missions that two of my Kings consecutively held the title of "the Killer". The first such King also was ranked 9/10 in every category except Piety, but he later became titled "the Crusader" because of his heroic valor in the Holy Land. At the city of Antioch, this King led an army of 10 units of knights to annihilate (that's right, annihilate!) two fully stacked Mongolian armies of 20+ units each (total 40+ veteran units!!!) led by a 7 or 8-star general that laid seige to the city in rapid succession. I admit that I was very lucky to have a quarter of my forces remaining after the two back-to-back epic battles. But my tactic and choice of defensive point was also crucial in this most unlikely of victories. You would also be interested to know that my current King has 10/10 rating in both Dread and Authority. But I digress because I'm so proud of my achievements.
Well after doing research for some time I found out the reason. When looking through my family tree I always wondered why all my faction leaders where evil. Assassins to me are new in this game as this is the first I am using them on a large scale.