As serendipity mentioned Plastikote is a good paint. Children paints probably shouldn't be used. If they say they are "non toxic" it doesn't automatically make it safe, non toxic to humans doesn't always mean non toxic to hamsters! You can also make your own dyes using vegetables or fruit. Here is a YouTube tutorial:
https://m.youtube.com/watch?v=U8q5B_grqI0
I've never used this method but you can make all kinds of colors using different fruits and veggies. Hope this helps