I've stamped and painted on tile with acrylic paints with ok success. You'll need to seal it when it dries (can take as little as an hour depending on the thickness of the paint) with a sealant. I used a spray matte finish like Kryon. I did find though that the paint is prone to getting chipped or nicked off, even after being sealed. Also, wipe the surface of the tile with alcohol to remove any residue that could interfere with the paint.
There are special paints available for tile and ceramic surfaces in the craft stores FYI that probably work better than acrylic, but I've never used them. HTH