Yes, use fabric paint. I recently used fabric paint on jeans (and bleach) and they turned out awesome. If you are in fact using the paint on denim as opposed to a cotton or such, it will seep in more (think canvas without gesso) so you'll want to take your time, have enough on hand, and make sure you put a garbage bag or board between any layers to prevent unwanted colour from staining another area of the garment.
Craft stores should have an array of fabric paint for you to choose from.
Good luck.
***side note, I used the same paint Corrine did in her mad hatter TB episode. It dries fast enough, but you can't wash them for 72 hours. and when you do ,inside out. Mine turned out great.