Sounds like they might be plastic laminate and if so, you probably won't be able to paint them very effectively. You might be able to get them resurfaced.

Try a primer called Stix - it's made to bond to plastic or other slick surfaces. You can get it in either brush-on or spray. It's available at most DIY stores. Make sure that the surface is VERY clean before priming (TSP or other paint prep cleaners work well) and give it a light sand with a 240 grit sandpaper. I generally like 2 coats of primer with a light sanding in between and then leave the primer to cure a week before top coating with a water based melamine paint applied with a foam roller.
Good luck!