You can take the celts/maya/ethiopia. However, this is rather limiting, so if you wanna play your favourite civ and still get a religion, you can
1) Ally a religious CS (including scouting hard to find one)
2) Use a religious natural wonder
3) Build Stone Henge (only with a v good start cos it's competitive)
4) Use a religious pantheon. (requires a ruin to get going or a shrine + meet religious CS (I've taken to buying my first), or heavy investment in shrines/temples with early expansion)
I find 4 to be the best, because it's more versatile and less of a craps shoot. If you can't do 1 or 2 and don't think you'll be able to go for 3, 4 is good because there are a load you can take -
1) Everyone knows desert folklore, get it with a desert start
2) Dance of aurora, get when on tundra, especially with hills cos you might actually work those tiles! If you're near tundra it might be a possible idea to move onto the tundra itself, cos with the pantheon the city tile will give good food/hammers plus the +1 faith for free off of a weak tile.
3) One with nature - get if you have a natural wonder nearby that isn't religious (if it is, it'll already be giving you the faith boost you need, so you can take MoG/FR for your pantheon), a second on the horizon wouldbe ideal. Particularly good with great barrier reef, which counts as 2 wonders.
4) stone cirles - Get if you can work approx 3 stones in a reasonable timeframe.
5) The one where you get faith from nearby wars. I like this one cos it's not terrain dependant, pick it if you start real close to some warmongers and expect an early DoW. Get good at inducing DoWs from reluctant would be warmongers. Nice cos you turn the most dangerous thingin the game into a benefit.
6) Less good but the one that gives +1 faith and + culture for wines and incense. Should only do with 3 or so such lux's, and will probably have to work in conjunction with shrines/temple builds here, but you get the culture boost as well.
Every one of these things is situational, but between all of them it's very rare that there's nothing you can do to aid your situation and get a religion. Just remember that if nothing else works out, you can usually sacrifice a MoG/FR pantheon in order to get a good founder/enhancer, which are the two best beliefs anyway.
Lastly, don't forget to think about the Hagia Sofia later on, which may be your best shot at getting the religious texts/itinerant preachers enhancer, which'll really make your founder work.