The previous owner of my car used that spray on dye stuff on my belts. After a few years, it had faded unevenly and made the belts go stiff. I had to buy another set of used ones. The new one were faded, too, but at least they weren't stiff.
I wanted to dye them, but do it right. I bought some of that Rit stuff at a fabric store, but the instructions weren't very clear, especially for nylon. I called their customer support 800 number, and talked to their engineer/chemist and asked how to dye seat belts. He laughed, and said funny I should ask, he used to work for DuPont in the seat belt group, and knew exactly how to do it.
I am sorry don't remember the details, but there is a process he told me and I used. It was something like mix the dye in water (precise amounts), then bring it up to some exact temperature (like 180 degrees). Then, chuck the seatbelts in, and cook them for so many minutes. At the end of that time, remove the pot from the heat, and stir in an amount of vinegar. Let them sit for so long, then take them out of the solution and put them in cold water.
It worked fantastic, they really do look like new. Again, sorry I don't recall the details, call the dye company and see if you are as lucky as I was to get routed to the right guy.