Here is a strategy that will give you a very good shot on a CV:
It requires very little commitment to that CV, so you can concentrate on other things (teching, getting Congress votes without interfering with your main plan).
You play as Byzanz. (Other religious civs work too, but require more dedication to gain quick faith, and have stil the opportunity to fail).
Since you are guaranteed a religion and your preferred believes, you don`t have to rush to a pantheon. Pick the one that you figure will provide you with the most faith over the whole game - you will need it.
Once you have founded, you want the following believes:
- Stupas
- second faith building
- third faith building (those two are not fixed, pick whatever suits you situation/playstyle best)
Also, found as many cities as you can - I aim for 20-30 on huge maps, on smaller maps less will do.
Pick piety. Once you have unlocked the 25% discount policy, start building every faith building in every city (starting with stupas). It seems daunting at first, but since every purchased building provides faith again, it is very doable.
Now comes the only part that is tricky: Get a reformation belief. Most of the times, you can grab Basilika (save a GE for it). If this fails, you need to go the hard route and get to 20% worldwide followers. It is possible, since your faith output is high, but you want to put the faith in buildings, not in missionaries. Of course you reformation belief is sacred sites.
Once you have assembled this, every city will provide 10 tourism (3x2 from sacred sites, +4 from stupas). Add colloseums everywhere and you are at 12 per city.
That doesn`t sound like terribly much, but you can have this tourism output from Renaissance on, where it easily overpowers contemporary culture output of AIs.
From there on, it is just a matter of watching your culture slowly but steadily overcome the AI.
General hints:
You are not in a rush to found a pantheon or a religion, but once you have set up, hurry to get your buildings up. The power of this strategy lies in the fact that you get your tourism so early.
Get Basilika. Did I say this already?
Meet all civs as soon as possible. You can only influence those which you know.
Be kind. You want to be friends with everybody, so you can open your borders (mind that you have to open your borders for the boost).
Your religious building will provide the bulk of your tourism, but don`t neglect other sources completely.
Try to have weight in the congress. There are very helpful resolutions.