1. Soak the eggs in vinegar/apple cider vinegar to achieve this affect.
Interestingly, they also bounce quite well at this stage (barely bounce with great care).
2. Use corn syrup to draw water out of the eggs (osmosis)
3. Use water and food coloring to re-hydrate
These eggs will be far larger than their original counterparts.
What is a science experiment without seeing the final result inside the egg?
As you can see, the yolk remained unchanged, while the liquid surrounding it absorbed a small amount of color. The membrane was completely dyed!
I would not suggest eating the colored eggs NOR using them as "color" bombs" ;)