There are polyester dyes, some regular dyes will take to polyester to a degree. Deep colors are more difficult, Rit brand tells you to double the amount of dye used for natural fibers. Some dyes are polyester-only I think, some only take to cotton, viscose and rayon, some only to silk and wool. There are some types that come in a jar, with a jel-like consistency, you pensil or sponge it on, it lasts but the treated spot turns out a bit more stiff than the rest of the fabic, at least on t-shirts and it takes to polyester too.