I am renovating a 30 year old house with ceramic tile. Is there a way to stain or change the color of the tile?

There ARE paints made specifically for ceramic tile, but especially where flooring is concerned, they're temporary, at best.

There is a process called "reglazing". I have a house built in the 1950's and the bathroom hasn't been updated since then. It's wall to wall tile and the color is disgusting. Teal and Burgundy. We're probably going to do it because we can't afford a full bathroom reno. It's a cost effective alternative. I don't think they will reglaze floor tiles though. Also, I don't think it's something you want to do yourself. I watched an episode of DIY's bathroom renovations and the guy wore a hazmat suit. Good luck on your renovation.