You can accelerate that if you are willing to DOW a religious civ and steal one of their missionaries. Sometimes you will see a CS with a captured missionary: DOW, steal misisonary and make peace in the same turn -- can be worth doing even if the CS is under another civ's protection, although that can can lead to a DOW, so be thoughtful.
Note that when you transport a captured missionary home, you need to make sure you don't lose him to attrition when passing through AI territory -- no attrition in AI territory with open borders, or in your own territory, CS territory, or no-man's land.