My daughters gave dying eggs with some of my old silk neckties a try. The warmer colors like red came out really nice, even captured the patterns on the tie. Blues didn't do as well.
The process is super simple, just wrap up the egg in the tie, tie it with string and boil.
Here is a Blog post with more details on the process => http://www.mommyknows.com/silk-tie-dye-easter-eggs-tutorial/