Place beets, onions and peeled eggs in a nonreactive (glass or plastic) container.
In a medium sized nonreactive (stainless steel) saucepan, combine sugar, beet juice, vinegar, salt, pepper, bay leaves, and cloves.
Bring to a boil, lower heat and simmer 5 minutes.
Immediately pour simmering liquid and spices over beets and eggs.
Cool to room temperature, cover, and REFRIGERATE 48 HOURS before using.
If the sauce does not cover the eggs completely, stir once in a while (I still get two-toned eggs; it adds to the enjoyment).
Serve with a slotted spoon.
This is a good side dish for picnics and barbecues.