I haven't used these, but Colorbox has a line of stamp pads for kids called My 1st Colorbox. They are made with child-safe inks and are supposed to wash off hands easily.
Here's a link:
Clearsnap » My First ColorBox Inkpad » Black
I looked online at Hobby Lobby and they are $1.99 each. They are $2.49 at joann.com but are only available online.