It all depends on the fabric. If it's organic-based, you probably can do it OK. Any of the poly/olefin based carpets... they're basically made of a plastic thread. The color is a part of the plastic. A pigment blended in before it's pelletized and extruded into fiber. The big problem will be finding something big enough to do it in. I have the same problem- I have a like new 35' cover that's an ugly wine color. Even if I could find a UV-stable dye, then find something big enough to boil the water to then dye it in, I don't thing it would take.
You might find someone that dyes carpeting. At the end of the day, you'll likely put alot of effort into something that gives you marginal results, then you're buying a cover anyway.
