Actually, what you get by doing that is what the Amish call "red beat eggs." But the eggs are not actually pickled, and have to be refrigerated. And, yes, they make great deviled eggs.
I like to really surprise folks by using my egg cuber for those. You wind up with purple colored egg squares. Usual first question: where do you find a chicken that lays square eggs. :smoking:
Anyway, here's the traditional recipe:
Red Beet Eggs
12 eggs
1/2 cup brown sugar
1/2 cukp granulated sugar
1/2 tsp salt
1/4 ckup water
3/4 cup vinegar
1 quart canned red beets and juice
Cover eggs with lukewarm water in a saucepan. Heat until water comes to a full boil. Remove from heat and let stand in water for 20 minutes. Run cold water over eggs to cool them quickly. Peel eggs.
Mix brown sugar, granulated sugar, salt, water and vinegar and heat until sugar is dissolved, stirring occasionally. Add red beets and juice to this mixture and pour over the peeled eggs.
Refrierate at least 12 hours. If the eggs aren't fully submerged, turn them from time to time to assure even coloration.