I would recommend the SanDisk Sansa Shaker. It looks a bit more like a toy, but from what I've heard it's more durable than most other MP3 players. If you would like video, you could look into the Spongebob Media Player.
Perhaps the best idea for your situation would be to provide your children with the least expensive option. In today's world, you can pick up cheap MP3 player for under $20, which prevents any large monetary loss. Currently there are no MP3 players available at a reasonable price that are hard to break.
The iPod Shuffle manufactured by Apple may be a great option. The 1st generation shuffles are small (about the size of a pack of Wrigley's gum), lightweight, easy to operate, and can hold a decent amount of songs.