You could try Dylon fabric paint, they have some paints specifically for painting on to dark fabrics. You want to find the sort that comes in 25mL pots like
this. Paint it on, allow to dry, cover with scrap fabric, iron to fix the paint, then wash (this is really for making the paint soft I think, so you might not need to do it for a bag).
I've used it on black fabric before, it won't work with a single layer. I'd imagine that just splattering with a paint brush would for the first layer, but then you'll have to paint over it by hand for the second. Use the iron on the first layer (once it's dry) before applying the second layer, and then use the iron again on the second layer (again, once it's dry).
Don't dilute the paint.