Req. Info. - Easter Egg Bread

Last year, I made a braided bread for Easter with the colored eggs in it. The bread was delicious, but I was not pleased with the eggs. I used food coloring on the eggs and the color ran off onto the bread when I baked it. I also read later that the eggs should not have been used raw. We never intended to eat the eggs and they were discarded as we ate the bread. Can anyone help me to be more successful this time? Thanks!