I have been trying for years to find decent ways to dye eggs naturally. If you are dying the shells, the flavor doesn't matter. But I like to dye the part you eat and make funky looking deviled eggs. This year, I tried for yellow on the egg white part. I read in a magazine to use carrot tops, which I cut up and brought to a boil in some water, then let cool and added vinegar before adding the eggs. I let them sit in the fridge for several hours. The result? Slightly off-white eggs. So I pulled out the old stand-by, and so far the only way I've found to dye eggs naturally: a chopped beet in hot water with a little vinegar. The longer you let the whites soak, the darker the color.
The photo here, taken this morning after the carrot failure, shows eggs that soaked in beet water for about 30 minutes. They are very hot pink and really don't look like anything natural at all, which is why they are fun to take to parties! I would have mixed some avocado in with the yellow mash, but my avocado went bad.