If you want it to be random, but you don't mind knowing who they are, you can always use random.org: You give every civ a number and roll random.org until you got the amount of civs you want. And because you don't give the civs you don't want numbers, you wont get those.
For example, I'm playing Rome and I don't want Ghandi in my game. There are now 20 civs left, so I roll a number between 1 and 20. I get 1, which is Alexander. So Alexander is my first opponent. Next, I get 20, which is Victoria. So she's my second opponent. Next I get 1 again, so I reroll, and I get 5, who is... and so on. (I only know the first and last civ in the list by heart...)