I know there are companies that will paint old tile, etc. They spray paint using basically a similar paint to car paint, they can do tile, bathtubs, appliances, etc. They paint everything, including the grout, so it would all be the same color.
How much tile do you have? Tile work on a wall isn't very hard to do at all. You could rip it out and re-do the tile yourself for not a lot of money. It would probably be easier then regrouting the tile too. To regrout, you have to dig out all the old grout and then put in new. It isn't fun.