"Cowboy Up" is when you are injured or down and the prospect of doing whatever it is you're about to try is so bleak that the best you can hope for is to live.
first of all to clear things up, cowboys aren't gay. brokeback mountain was a movie about sheep herders, not cowboys. if anything most cowboys are gay.
This Slang page is designed to explain what the meaning of cowboy up is. The slang word / phrase / acronym cowboy up means . Online Slang Dictionary.