Actually if you want to do it properly you won't want a product that shines, or comes off after a heavy rain.
On my black trim, and my tires I use Adams Super VRT
Best Tire Dressing | Super VRT | Car Detailing Supply
I know you're probably going to say "shit I can get back to black at walmart for cheap, or use tire shine" but that shit doesn't last. I'm 27 now, I bought a bottle of Back to Black 10 years ago, used it once and threw it in the trash. It sucks. Using tire shine products on your black trim, sucks. Unless you like that armor all sheen on everything, and having the surface feel sticky since they are mostly petroleum based products. Don't dye it either, maybe you should use the "WIPE NEW" stuff on the commercials lol.
Seriously though, the Adam's Super VRT leaves everything a matte black, crisp finish, watch the video on his website, I'm telling you it is worth the price. The key is you have to clean the hell out of your tires/trim before applying, the product only works as good as the prep. You are going to still have shitty looking trim if its not cleaned well, and your tires will look like crap if you don't get the old armor all/hot tire shine crap off there too. I actually use the Adam's All Purpose cleaner with a microfiber, wipe down all my black trims on the car, and scrub the hell out of my tires. Then using an applicator pad for waxing or sponge type, I go over my tires/trim with the Super VRT.
It's water based, so its not greasy, it has friggin sunblock in it for gods sakes, and its waterproof up to a certain amount of time. I usually only have to redo the trim every few months or so, hell, I don't even redo my tires every time I wash the car. But the trim looks brand new, and it stays looking that way, and water beads up off the trim like it has wax on it, really is amazing stuff.
If you're looking to step up to a legit way to get the trim looking good again, you'll use the Adam's Super VRT. All the rest are just products for boys.
EDIT: Here is a complete kit with the VRT, the all purpose cleaner for cleaning everything first, and applicator sponges:
Tire Dressing Products | Super VRT Tire and Trim Kit