An allied CS has a quest open to get my religion (Atheism). The CS is mostly Christian (the enemy civ) so when I try missionaries, it does not affect it very much. So I got an inquisitor to try and get Christianity out of the CS. My unit is right next to it, and there is no option to heresey or anything. Am I doing something wrong? Is it impossible to do to CSs? Do I just have to throw piles of missionaries at them? Thank you.
As noted in this answer, inquisitors affect your cities. Based on my understanding, since you don't own city states (you befriend or destroy them) the inquisitor would seem to have no jurisdiction over them.
The most effective form of conversion is by applying pressure through neighbouring cities. Convert the cities near the city state (within 10 tiles or 13 if you have the correct upgrade) to your religion and the pressure the neighbouring cities apply should convert the city state to your religion. If neighbouring cities are applying pressure of a different religion, then the effects of your missionaries will be counteracted relatively quickly. In order to convert a city that already has a majority religion, it will take the pressure of two or more cities.
If you are unable to leverage the religion of nearby cities, then you will be sending a great many missionaries. You can also use great prophets for a faster conversion.