I want to color my zinc metal alloy pendant with the most permanent blue paint for metal that anyone knows. Any opinions? I know they use chrome paint for metal cars and anodized stuff for aluminum, can anyone help me with this?

The simplest way would be to:
1) Sand the surface lightly with a fine (1000 grit or finer) emery cloth -- Paint needs something to bite onto and won't stick if the surface is too smooth
2) Wipe it down with a de-greaser and Metal Prep, which any auto parts store would have
3) Paint (or dip) the piece in a good etching primer
4) When it dries, sand it a little more to get a good surface for paint to stick to
5) Give it a couple light coats of a good quality automotive acrylic -- The auto parts store or you local car dealer should have little spray cans of touch-up paint that will work nicely

The next step up with be a catalyzed polyurethane (such as Dupont Imron) made for high end cars and aircraft. It lasts forever but be warned, it is deadly stuff
Beyond that would be baked finishes like e-coat, powder coating, and porcelainizing (the paint on a stove