Basically, every costume has an alternate version for the player 2, just in case both players pick the same costume. The color scheme is usually the same-ish as the one from the player 1. But sometimes you get some interesting alternate colors.

To pick the player 2 color, you have to:

1- hover the cursor over the character
2- open the costume select menu
3- highligh the costume you want
4- select it using the start key, which is usually the number 4 on the keyboard.

Here are a few interesting colors I found:

Superman - Lockdown


LexLuthor - Insurgency


Killer Frost - Base costume


That's all, folks. And don't forget to...