I'm not really an organic chemist (heh, heh) but I've dyed eggs with natural colorings. It's pretty fun!Colored Easter Eggs Using Natural Dyes
By Anne Marie Helmenstine, Ph.D., About.com Guide
It's safe and easy to make your own natural Easter egg dyes from common foods and flowers.
It's fun and easy to use foods and flowers to make your own natural Easter egg dyes. The two main ways to use your own dyes are to add dyes to the eggs when boiling them or to dye the eggs after they have been hard-boiled. It's a lot faster to boil the dyes and eggs together, but you will use several pans if you want to make multiple colors. Dyeing the eggs after they have been cooked takes as many dishes and more time, but may be more practical (after all, most stoves only have four burners!).
Try both fresh and frozen produce. Canned produce will produce much paler colors. Boiling the colors with vinegar will result in deeper colors. Some materials need to be boiled to impart their color (name followed by 'boiled' in the table). Some of the fruits, vegetables, and spices can be used cold. To use a cold material, cover the boiled eggs with water, add dyeing materials, a teaspoon or less of vinegar, and let the eggs remain in the refrigerator until the desired color is achieved. In most cases, the longer you leave Easter eggs in the dye, the more deeply colored they will become.
Handy table of ingredients at the link.