The recipe I use was my grandmothers and I beleive it was her mothers, my great grandmother (she was Amish).
PICKLED BEETS AND EGGS
1 dozen hardboiled eggs
1 16 oz can beets, sliced or chunked
1 cup apple cider vinegar
1 cup sugar
1/2 tsp. ground cinnamon
1/2 tsp. celery seed
1/2 tsp. ground cloves
Peel eggs and put into a container that can be sealed, I use a Tupperware bowl. My grandmother used a widemouth glass jar. Drain beet juice into a saucepan, add the vinegar and sugar. Bring to a boil, stirring to disolve the sugar, remove from heat and add the spices. Mix well.
Pour the canned beets over the eggs and the the hot juice over the beets and eggs, refrigerate for 2-3 days.
These are wonderful, I make them about once a month. The eggs really absorb the sweet/sour taste because the juice is hot. It's like putting mayonaise on hot potatoes when making salad. The flavors are much deeper. And the red beets have a marvelous flavor too.