Dont just use ANY black paint, but go to an automotive paint supply store, and buy a can of this stuff....
Klean Strip Bulldog Adhesion Promoter
Spray Max Trim Paint Satin Black
Normal rattle can paints will not hold up to UV deterioration. This stuff is great for trim, wiper arms, old faded plastic mirrors, door mouldings and trim, etc. It comes in flat, satin, and gloss. Since most trim on cars is satin, that's what I chose. I used it on my little 89 Accord on the B pillar trim because it had become faded and not even a thick coat of Armor All would help it.
Do like said, and wet sand down the trim to make it smooth, use a scraper to remove any flaking coating as well and sand it out smooth. Get a can of DuPont Final Clean wax/grease remover, wet a rag and wipe it down to remove all oily contaminants that could cause fisheyes in the paint. You may want to wipe it down with a soaked cloth, wipe it dry, then use a new soaked cloth and do it one more time just to make sure you get it all.
Prime the area with the above mentioned adhesion promoter, a light coat, wait 5 minutes, and apply one more light coat. let it set for at least 20 minutes. Then, apply one light coat of the Spray Max trim paint, let it flash for 15 or so minutes, then do another light coat, let it flash for 20 or more minutes, then do a final coat, trying to get the surface nice and even, a bit heavier than the first two coats, but not so much it runs, just make sure it's even. Then let it cure for a day or so in the sun, and it will be fine to put the trim back on. Really easy to do!!
Here's a few pics of the trim I did on the Honda.....
Sanded and masked off, and wiped down with Final Clean..
Three coats later.
Unmasked and admiring my work....