Dyeing a rabbits fur, for any reason, requires using only food coloring mixtures and never conventional hair dyes. Regular hair dyes can burn or irritate skin, so it is inhumane to subject any animal to that feeling. Using diluted food coloring in water and a sponge to apply the mixture is the safest way to change the color of a rabbits fur. The rabbit will also constantly lick it's on fur to clean it, so the coloring will not effect it's digestive system as a harsh dye would.
Fill a large bowl with lukewarm water almost to the top. Add food coloring three drops at a time. Wait after each set of drops and allow the color to diffuse into the bowl and settle. Continue to add coloring drops until the desired color is reached.
Put on latex or rubber gloves. Dip a soft sponge into the food coloring and allow it to become soaked. Pull out the sponge and ring out half of the excess mixture. Place the sponge on just a small part of the rabbit to test the color. If the color is dark enough, continue; if not, add more food coloring to the bowl.
Dip the sponge back into the mixture and again, ring out half the excess. Brush the sponge over the rabbi's fur to change its color. Continue this method until the desired area of the rabbit is covered.