Civs that you definitely want to add in:
1) Poland: Just, a great civ, a great UA, the bonuses are enough that the AI usually does a pretty decent job with them.
2) Greece: The addition of Greece in the game makes city states that much harder to take. The game is very different when Greece is or isn't in there, and much more difficult when Alexander creates his alliances with all of the city states.
3) Iroquois: I'm not sure why, but the AI does well with them. Just the right expansionist flavors for success I guess.
4) Zulu: Probably the best warmonger AI civ in the game. He'll be a pain to someone. It may be you.
5) Siam: Same reason as Greece. This guy will just plain out annoy you, steal all your city states, and be generally strong but tough to kill.
And.. For the other civs, idk, none of them strike me as particularly amazing in the hands of computers, so take these suggestions as less decisive.
6) Russia. They're a nuisance, get a pretty strong religion, and will attack you as soon as they run out of expansion room. Expect backstabs from them.
7) Ethiopia. Good luck establishing a religion if they start off near you. I think I just saw another missionary. Wait, no, that's another five missionaries and a great prophet. And they're all headed towards your capital.
That's probably what I would choose if I were choosing a standard game with seven AI civs. That would be a pretty tough game.
EDIT: I just remembered, Spain is another potential option. Isabella is my personal nemesis in civ. They don't always cause problems for me, but they've caused me some memorably miserable games.