Brenda, I have to admit it is not something I would like to try and attempt. I'm guessing with a good clean it might have a chance of sticking, but from memory the plasticised surface is slightly textured. A combination of this and the curves things leads me to say I don't think it would be good for your mental health to attempt it.
Why not clean and degrease the surface, use an all surface or melamine and tile primer then paint with an acrylic/water based eggshell paint.
Colin