There is a product that makes linoleum block printing totally doable with kids. 
It is a very flexible material that can be carved without the strength needed for the old linoleum blocks of the past.
The product is called Grafix® Shrlnk Film found at http://www.enasco.com
Have them use a pencil to firmly draw their image in.
Draw, cut, and bake! Just draw on a sheet of film, cut it out, and pop it in the oven and watch it SHRINK for miniature ornaments of their design. Remember to hole punch a hole before shrinking though.
