Don't get the stuff that you buy at halloween stores. She'll smear that too easily.
Get Mehron Paradise Paint. It's water activated face paint that when it dries won't smear badly if she rubs it. It washes off with just water. It's coconut oil based, so it won't hurt her skin.
My my my, don't you sound like an authority on clown makeup. When was the last time you were in Alabama?