I have some thin tyvek which I painted (kite tyvek). I used acrylic paint, as in art supplies paint. It has stayed on for four years. The only down side is that paint is heavy. Too much of it will make your tarp heavy and stiff, I think.
Tyvek also stains. I want to try stain on it, like walnut hull stain, or beets. Dirt definitely stains it. Try rubbing red clay on it. If you don't have any, just ask anyone in my part of the country for some.