Here's Grandma's

For a large jar, I usually double or triple this:

To a large stainless pot (stay away from aluminum with acidic mixtures) ADD:
1# canned beets with their juice (clean em to get rid of spots and ends)(plain small beets, not harvard, etc.)
1 cup vinegar
1/4 to 1/3 cup sugar (white or brown)
3/4 t salt
Optional if you get tired of the original: cloves, cinnamin, pickling spice

Bring to a boil, then let cool a bit.

Pour over shelled hard boiled eggs. All eggs and beets must be covered by the liquid.
Refrigerate. Wait a couple days then sample. When the color starts soaking into the yolks, ya got a winner.

Not sure of the shelf life, but have often added more hard boiled eggs as the level drops.