Black oil-based rustoleum should be perfect, and it will not encourage any rusting. I'm assuming it already has old paint on it. If it has been stripped, you should use red oxide primer first.
Casey

Using exterior latex paint indoors can cause health problems for some folks due to the higher mildewcide content. A co-worker of mine learned this the hard way.

Good to know, jessicaml, thanks! The tub doesn't seem to have any paint left on the outside, but also isn't rusty. Rustoleum says not to use the red rusty metal primer on non-rusty metal. Is there another red oxide primer I should use? I'm going to have to do this all with brushes, as the bathtub is going to be in my very tiny and very recently decorated nursery (no, the baby won't be there - he's out of town), so spraying is not very practical.