Powder coating is for metal. The metal gets hooked up to a power source that makes it electrically charged. Then when the plastic powder is sprayed on, it gets attracted to the charge. Then the part gets baked in an oven to melt the plastic particles together. I'd think that last part could be difficult without warping the plastic part to begin with.
When sanding, the method for getting a perfect result is to use progressively finer sandpaper, with a cleaning in-between each. Each successive step should be with less than twice the grit than the step before.
I think I would just spray it with black spray paint myself. Spray even thin layers, and let each layer dry before applying the next.
But the paints used at an auto repair shop could be more durable though, sure....
I had spray painted my daily driver a few years ago, and the paint on it is quite worn by now.