Sure. Good question.
They make a plastic paint that works really well. Body shops use it all the time on bumpers and trim. They have a variety of colors. I used to work at a body shop and I've personally used it a bunch. You want to get a good quality paint made by SEM or another company that serves the industrial business. It comes in a spray can. Probably buy it on Amazon or Ebay. It's more expensive than most spray paint. You might need a primer, not sure. Follow the instructions to an absolute "T". Make sure to mask off really well. I'd personally cover the car in plastic b/c it's a lot easier to buy a $3 piece of painter plastic than spend 2 days removing overspray. Buy good quality 3M (yellow or green) masking tape that removes easily (but no risk of lifting paint), not the el-cheapo stuff. You probably don't like the idea of painting over plastic, but once it's UV faded, it's a viable long-term solution.
What a guys DOESN'T want to do is use wax or any kind of silicone appearance product like Armour-All, STP, etc. I mean you can, but it's short-term as you've found out. Silicates actually kind of goof up plastics and rubber. If you HAVE used either of those recently, you might put the job off a little longer a couple months ..and let the weather and rain remove most of the residual, especially if any gets between the micro-cracks in the plastic ...or thoroughly use a wax and grease remover. Paint not only DOESN'T stick to wax or silicates, it repels it. If you try to paint over plastic that still has wax or silicates in it it'll look like total crap b/c it'll fish-eye all over the place and generally not adhere well. Keep silicates away from your vehicle and it'll be happier in the long run.
The first coat should be a somewhat 'dry' mist which will lessen the chances of fish-eye on subsequent coats. Then the next coat (wet) should lay out nice. Don't overcoat. Don't use common el-cheapo spray can paints b/c they don't have enough UV inhibitors to stay looking black (or brown ..whatever color yours is) long enough. The temptation to save a few bucks is high, but I personally would only use the good stuff, but it's like $18-$20/can. But still, 1 or two cans is probably all you'll need. SEM has some videos on youtube I believe.
If you do it right it should look great for a long time. I have bumpers I've painted that look good 8 years down the road and counting (never garaged).
Good luck, report back your results!!