It depends on what it is mad of, Terri. If it's wood, any paint should work, just be sure to do your prep-work first.
I usually use chalk paint on frames. Acrylic works, too.
Any paint works. If it gets on the mirror part, it can be scraped off with a razor blade and it won't damage the mirror. I normally score it along the seam. If you're having a hard time with the little bits of paint, windex and a paper towel helps.
Chalk paint is a great option heres a tutorial if you wanna make your own and not compromise on color!