I have painted tile that was not subjected to water. You will need a primer that will adhere to the slick surface of the tile. Then you can paint the primed tile. Go to www.Zinsser.com to find a suitable primer. Then use a good quality paint.
I also agree with the previous suggestion of re-tiling. I ripped out a tub suround recently and re-tiled it. If not sure how to proceed you can get a book with detailed instructions at a Home Depot.