I'd would use dye over paint any day. Since it's black, maybe try bleaching it first so that the blue dye will take to it better. I'm assuming this is a typical military utility belt, correct.
Have you looked into just finding the same material in blue and making a new belt? Might be easier.
yeah its a type of ammo military belt, i'm trying to make captain america's belt from his suit in the avengers movie, i can post a pic of ithttp://www.armyshop.com/prodimages/thumb/fo-50-36-thumb.jpg.