Yes, sure they can be painted. You must first prepare the surface properly. Sand lightly and then wipe off with a damp cloth. Then apply a good primer. Bulls Eye water based LOW ODOR PRIMER is great cause it eliminates a lot of sanding. Then paint with any water based wall paint. For more durability, use a top coat of water based polyurethane. Make sure to read instructions. Faux Painting can be a great alternative to a solid paint color. I did a counter top and it looks fabulous. Here's a close up picture. It's just simple sponging.
Here's a website that shows you how to faux paint a marble finish, too. The good part is that you can always just paint over.