There are some rare, but very specialized faux painters that can cover the tile and create a whole new look. They can change the look of the size of the tile and give it a whole different look, color and texture. My guess however, is that the cost would be comparable to installing new tile. The difference would be that you don't have to go through that mess.

Find an experienced painter or faux finisher. He can use a great primer then paint over the tile, then seal it. I've done that when custom tile came in the wrong color. Shouldn't cost much.

I would suggest under cabinet lighting.