Is the surface plastic? Dupli-Color makes all kinds of paint and related coloring products for cars. One of these might be right for putting the black on your screen. Plastic can be painted, but it wears off. Dupli-Color has some plastic dyes that last longer. Use at your own risk!
For the record, I've used a black Sharpie to touch up chips in the paint of my black car. It works amazingly well!