Chris's wife Katrina suggests:
The dye kits for Easter eggs are scary. The dyes can stain EVERYTHING: kids' hands, floors, tables, and the occasional egg.
Just as attractive and definitely a lot easier to clean up is the idea of using a kid's set of watercolor paints to decorate the eggs. It's just as exciting, a little more hands-on, and downright easier to clean up after.
I didn't grow up dyeing eggs. Painting them seems more fun to me anyway.
If you're a traditionalist, though, consider using a whisk to simplify egg dyeing for kids.