In theory, articles dyed with RIT must be done so in warm or hot water by soaking in the RIT solution. It is my understanding that failing to do so will result in the dye rubbing off. I dyed some fabric welting along the door seals in my 240D using the incorrect in situ technique and the result was OK. Some dye wore off, but some remained. Overall, better than what was there but not perfect.
Another option would be SEM upholstery spray for vinyl/ leather. Some people have used it for carpet.