Hi,
Since you aren't trying to change the color of the caps, I'd suggest trying to clean up and polish the plastic before resorting to painting it. That would be more durable than most paints, *if* it's possible to get them to clean up adequately. Then, if you can't get them to look good, you can always fall back to the repaint option.
Plastic supply stores (like TAP Plastics) and other places sell compounds to clean and polish hard plastics, which might work. These are pastes that come in small bottles, and are offered in different grits for heavy or light scratch removal and final polishing by hand. Eastwood also sells a number of different plastic refinishing compounds, but generally for power polishers. Different products work on everything from turn signal lenses to convertible top windows.
If you go to a local plastic specialty store to look for these products, it might be wise to take along one of the center caps. They might be able to best recommend what will work on it.
There is also a wide array car cleaning products specifically made for plastics and rubber that might help. Armor All is probably the best known. The problem with many of these products is that they contain silicone, which will make any later paint application a lot more difficult. I'm not sure I'd recommend trying these, unless you are certain it will work. If you want to try, experiment on a hidden area first to see if it will do the job. That way you won't have the extra prep steps of removing the silicone before painting, should it come to that. Also keep these cleaners off the area where the sticker will be placed. The silicone will likely keep the stickers from adhering well.
Sometimes plastic "fades" deep into the surface, and none of the above ideas will work. Then, painting might be the only or best choice. You've gotten a lot of good suggestions about that.
Cheers!
Alan Myers
San Jose, Calif.
'62 TR4 CT17602L