Prepare a canning pot and enough jars to hold 4 pints of pickled onions.
Bring a large pot of water to a boil. Add the sliced red onion and cook for four minutes. Drain and set aside.
Using the same pot in which you quickly cooked the onions, combine the brine ingredients. As soon as the salt and sugar are dissolved, add the red onions. Stir to combine and remove from heat.
Remove the jars from the canning pot. Fill with the onions and brine, leaving 1/2 inch headspace. Use a wooden chopstick or the end of a wooden spoon to remove as many bubbles from the jars as is possible.
Wipe the rims, apply the lids and rings, and process in a boiling water bath canner for 10 minutes.
When the time is up, remove the jars and set them on a folded kitchen towel to cool. When the jars have cooled enough that you can comfortably handle them, check the seals. Sealed jars can be stored at room temperature for up to a year. Any unsealed jars should be refrigerated and used promptly.