K.F.
If your vet doesn't do it, or if you just want to do it yourself, I'd use washable tempura paints like crayola makes, although there would be other brands which surely would be fine. A heavy paper would be best for durabilities sake. If you go to an art supply store you would look for a paper that is archival quality, basically low acid so that it doesn't yellow and degrade as easily. Those types are easy to find. Nothing shiny as it won't take paint easily, you'll be looking for a matte finish. Beyond that, it's really just preference.