Here's a look at the pious custom of red eggs in the Orthodox Church for you and your families to enjoy. Where did the tradition come from anyway? It seems there are a few possible answers to this question...of which I prefer to believe in the miracle that God worked through His handmaiden, Mary Magdalene (whom by the way is often wrongly attributed as the prostitute who anointed Jesus' feet and wiped them with her hair - See Orthodox Wiki for a well cited clarification).
Other symbolism, not as dogma, but as tradition includes:
*The egg as the new life in Christ through His resurrection
*Red for the color of our Lord's blood but also for His divinity
*The outer shell to be cracked as the doors of Hades are shattered
Since children enjoy decorating the eggs, why not encourage them to display their faith on them, as the picture shows! Be sure not to throw away any icons if you use them, but certainly include symbols like ~ icxc, fish, crosses, tree of life, the Trinity, 4 Greek Letters for Mother of God...etc
You can write on eggs with melted wax, then dip them in red dye, and afterward, burn off the wax to reveal the design underneath.
This worksheet is available in PDF format here