Place beets, onion, and peeled eggs in a nonreactive glass or plastic container. Set aside.
In a medium-size nonreactive 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.