A few years ago, I dyed the faded factory seatbelts in an old muscle car. I used Rit fabric dye that you can buy at any grocery or walmart. They came out great and there were no problems with the color bleeding after they dried. I used warm soapy water and a scrub brush to clean them first. Then I followed the directions on the Rit dye. I was very happy with how they came out and I am very particular on stuff like that on my Nova's. I used black dye but I'm sure they have red as well.
My 03 Rubicon build thread ---> http://www.jeepforum.com/forum/f22/1320quicks-03-rubicon-build-1504699/