I am confused. What are you trying to achieve? What kind of fiberglass door? Is it coated now or is there just colorant in the fiberglass?
I think the problem you are going to have is the polyester resins that were probably used to form the door. I don't think you will get any kind of stain to penetrate. You could paint but you will need a plastic primer first. Rustoleum makes one that comes in a spray and in liquid form. You might get some sort of Melamine paint to stick directly but it would be risky.