This year I tried using turmeric as a natural egg dye. I heated up some water, added vinegar, and poured in a bunch of turmeric. Then I put a rubber band around the egg (the kind broccoli comes in) and put the eggs in a container in the fridge for awhile. The second batch was in much longer than the first batch, and the length of time didn't seem to matter a whole lot. This is about as dark as they got.
Also, I'm not convinced that heating up the water actually does anything.