It should still be possible to clean the headliner if it's just dirty. I had good success on mine using things like a solution of baking soda/water (but careful with drops because it will tend to leave white traces everywhere), magic eraser etc. And your standard clorox wipes too. It takes a while and you'll have smudges until you really clean it all up, but personally I wouldn't want to deal with having to paint a headliner inside a car. Spray paint will get on everything.

If you want to turn it to black, maybe something like Forever Black (dye with applicator) would work. Since the headliner is textured and porous, I don't think it should streak too much.