I can only imagine what a horrible project it would be to try to dye the carpets. First you are going to want to pull the seats, right?
Well, at that point, I'd think it would be much easier to just rip the old carpet out and put some new carpet in.
Now, FWIW, if your carpets are just dirty, go get one of these:
http://www.amazon.com/BISSELL-ProHe...22&sr=8-1&keywords=little+green+steam+machine
I've had one of these for years, and the first thing I do is clean the carpets of my vehicles. It does a GREAT job of getting dirt out. Some trucks, most notably the ones with red carpet, actually made the carpet look new again. Tan, not so much. YMMV, but I love that little guy. Plus you can clean your seats. Just read the manual so you do it right.