Suggestion....If you're going to use Rit dye make sure to use the appropriate amount of Rit dye fixative so that you get minimal bleeding. As Steve suggested, for black you're going to want to double the formula and leave it in the dye bath for a longer period of time for maximum penetration. Multiple rinses to keep the bleeding down although the more you rinse it the more your chances of it coming out charcoal instead of that deep midnight black.
If it was me I would send it to a professional dyer. They have the appropriate chemicals and industrial dyestuffs to get your belts as deep black as they can. Rit dye tends to fade after a while since it doesn't penetrate the core of the yarn as deeply as professional dyes do.
What type of yarn were your belts made from? It they were made from polyester then it will be harder to dye them as poly doesn't take to deep colors all that well. It'll be more of a charcoal than a black. If they're nylon then you're good to go.
I used to own an industrial dyehouse so I know a thing or two about this stuff!:yes: Expect to pay anywhere from $35 - $50 to have it professionally done. Dry Cleaners will claim to be able to dye them but they usually just use Rit dye also so I wouldn't waste my time with them.
Too bad you aren't closer to me. I have several industrial dyehouses that I use for my work. I could have them include your belts in a load of garments that they're dying black for cheap. They dye black on a daily basis.
John