What about using a waterproof vanish. Any varnish suggested for use outdoors, like a deck sealer, will work. The main issue, I think, would be making sure it doesn't discolor the images.
You could also use a coat of resin, which will give it an almost domed look and make it feel kind of like a hard rubber on the top. It also has the bonus of being absolutely waterproof, not damaging the images, and providing a non-skid surface. I actually found a site that gives detailed instruction on how to make the type of coasters you want using resin.
Diary of a Crafty Chica: Resin Coasters