Painting metal frame in bathroom shower stall?
If you REALLY want to change the color and be SURE that it will hold, then having it powder coated is the answer. In fact, many shower door companies use powder coating. Word on the street (or internet) is that spray paints won't stand up to the moisture and cleaning over time.
Powder coating is a process where a powder is sprayed electrostatically onto the piece and then the finish is baked on (about 400 degrees).
You would need to completely dissassemble then entire frame and take the metal pieces (screws and all) to a powder coating shop. You will have the choice of 20 kabillion colors and effects. They should be able to do it in anywhere from a day to a week depending on their schedule.
I did this with my old polished brass colored (anodized aluminum actually) frame that was L-Shaped (about 3' x 4'). It was A LOT OF WORK, but, cost me only $150 vs. about 8 to 10 times that ($1,100 to $1,5000 to replace it. I took pictures and videos of the disassembly and made notes of where every little piece went, etc. Fortunately, all of the rubber sealing strips were re-usable. I put the screws in a piece of cardboard so they would stay in one place and those were powder-coated also (wood instead of cardboard would have been better).
This was part of a full bath remodel where the old shower walls and tile was all replaced, so, I had to be sure it was built to accept the existing shower frame. That's bass-ackward form how it's normally done when the shower walls and tile is built first and then frame/glass is built to fit that. So, that was a difficult process.
Re-assembling it all was tough also. The notes, photos and videos paid off. It was a LOT of work and I might recommend just buying a new one instead, but, if you have the time, patience, ability and inclination then have at it.
We've been using our for a couple of months now and I have even scratched it a few times, but, nothing happend to the finish. It's pretty tough and it looks great and like it's brand new.