Another thought is that you could have cultured marble, which is a type of solid surface made from a mix of polyester resin and marble stone dust. In all my years in the remodeling industry, I have never seen anyone paint cultured marble. If you search online, however, you will find instructions for doing so. If you have cultured marble and wish to paint it, I would advise you to first check with the manufacturer to see if this is possible, then talk with the owner of a paint store for information about the proper preparation, primer, and paint.