Hi Laurie, Cheryl gave you one of the best video I watched on dying carpet. I watched quite a few and the one with the lady with the dark hair seems to be the most informative and helpful.
I love the idea of dying a carpet using a rag and some diluted RIT dye. But I also LOVE the idea of painting it even better. You can buy fabric paint right at Micheals. But what I would do is buy ANY COLOR latex paint and add a fabric medium into it. Try liquitex fabric medium or ceramcoat textile medium. Paint has so many more colors to choose from and being able to pick my own color and turn it into a fabric paint sounds even more fun. I haven't done this yet so I don't have one of my own posts for you but I have thought about doing it myself and I would use these products.
Years ago, I had carpet dyed at a commercial property by a carpet cleaning pro who was reasonably priced; it turned out GREAT ! If it gets to be TOO BIG of a job for you to do solo, you can probably get a FREE estimate. Sometimes, when the price is right, i just let somebody else do the work, and i sit back and enjoy the results. Best wishes on your project!