Try a black permanent marker or fabric paint. It's the easiest place to start, and if you're satisfied with the results you don't have to go any further. Keep the marker or paint handy -- you may have to reapply after several washes.
Bleach the entire garment so that it's mostly the same color throughout. Degrade the bleach with an oxygen boosted bleach or hydrogen peroxide. This is an important step because you don't want the bleach to eat away at the fabric. You can use Rit Color Remover as an alternative to bleach.
Purchase a dye that is appropriate for the fabric type and dye the garment according to the package directions.
Cover the area with a patch if it wouldn't look out of place and you are determined to get more wear out of the garment.