I buy baskets full of the hair dye stuff around halloween. Makes for fun playtime stuff when the kids are bored. I also use it for fun shows.
For black I have heard of shoe polish....there is also dye that you mix in a bowl and brush it on, that may be an option for you. But I would do more research on that before putting it on your weanlings face. Though I also would use caution around the eyes. Any of that stuff is still chemicals and can cause trouble.