I have painted accents on powdercoated frames a couple of times. Here's an example where the frame is powdercoated blue and I painted the lugs black.
I just did a bit of sanding and masking and did several coats using gloss rustoleum (I think) and clearcoat. Be sure to let each coat dry completely before doing any sanding or another coat. Also, use long, smooth passes, laying down a light layer of paint each time so that it won't pool and drip.
For your situation, I wouldn't really recommend spraypainting. Regardless of the brand and technique, the paint is going to chip, and if you're painting black over white the chips are really going to show. You might be better off just having it powedercoated again.