i tried making red dyed eggs some time ago for my friend. here are the steps, hope this helps
1. select the eggs with light colour - this will make the colour look smoother
2. boil the eggs for about 15 mins.
3. while boiling the eggs, prepare water and the red dye (using food colouring agent - choose something like pink rose), i wanted to make pinkish eggs, so i only drop a few into the water.
4. let the eggs cool down for a while
5. dip the eggs into the dye, make sure the water covers the eggs entirely
6. let them sit for around 3-5 minutes
7. dry the eggs, voila you got pretty pinkish eggs!
i think pink eggs look much prettier than those solid red. i dont know if this is okay with the tradition but my granny said as long as the eggs look pink or red, it's alright.