Food coloring works. Just make sure you put the dropper portion within the vent and squeeze a bit. Just don't hold it over the vent and let it drop down, I had better success with the dropper inside. The vent pulses and that helps to draw the color in. For most, you get a tiny speck of color somewhere on the egg. The red color had the best result and it was the one I put the dropper into the vent. It colored her eggs for a month, most of the others were colored for a few days.
Make sure to label the food coloring box "chickens" or something like that otherwise it would be a mistake you would never forget.