ONLY convert the biggest pop cities!!! Then try to convert cities that are at the ends of a river... (this makes a monopoly of trade route spreading)
The AI will rarely if ever spread their religion in the early game with missionary... Unless they're Ghandi and Egypt...
What you should do is open border with everyone that you want to convert... Don't open to buddah founders and hindu founders if you aren't one of them... Cause they will generally have that religion spread among itself as soon as they found it...
Once you get organized religion, just start pumping out missionaries like crazy and head for the capital of each civ you opened with... Then head for a 2nd city that is the biggest you can find...
Once you do that, start gifting them missionaries... If you're trapped between two AIs and can't spread your own missionaries, the AI will spread them if you gift them yours...
I posted a game recently that had about 9/17 civs under confusionism... (including me)
In my current game, I got 5 / 16 under chritianity...
With Qin also... So no mysticism start...
Noble Epic... (epic should make spreading religion easier since you get more steps between build sequences...) On normal, build times and the game is faster, so you generally lose steps overall... Having more civs and less map space helps too... This means you'll have many more civs that will have no religion to start... Also they're closer together... If they're far apart, a single missionary will spread a lot of religion since it'll take forever for someone else to influence them...
Having the AI convert don't mean they'll stay... To ensure they stay that way (the only good part about religion) is to keep their whole population under your religion... To do that you MUST make missionary to convert the other cities... So with that said, just because the AI is under a religion don't mean they'll stay that way either... Just make them happy and keep sending missionaries out to their biggest cities... They'll switch out once their population majority (and political if you're asking) values are great enough...
One last tip... It's a HELL of a lot easier to spread your religion to another civ if you don't have a conflicting state religion... So if you're nuetral spreading the religion you found, more civs will likely open their borders to you... Since they won't think you're a heathen... Once you spread the religion as much as you like, then switch yourself...
This sets up one HELL of a diplo win... Just beeline to UN wonder and watch your win come closer with each tech you gift to the AI...