Looking for recipes for green tomatoes on the internet I tried this one Posted on October 9, 2012 by sheldonlaw (find the original link here >) which let me make pickles that didn’t involve canning.
According to the post they keep about 6 months in the refrigerator but (see cautionary notes below):

 

Korean Green Tomato Pickles

1. CLEAN and towel dry small to medium green tomatoes – Fill any glass jar available, about a quart size – about 3 lbs of tomatoes

2. POKE tomatoes with a toothpick several times – top, bottom, side to side depending on how big the tomato is

3. Add 1 cup of water, 1 cup of soya sauce, 1 cup of sugar, 1 cup of vinegar, and 1/2 cup of wine to a large pot and boil the mixture and a tablespoonful of red pepper flakes (optional)

4. Let it boil for about 5 minutes then remove from heat and pour into the jar full of tomatoes

5. The mixture should cover the tomatoes, if it doesn’t, make some more and dump it in there!

IMPORTANT: Pour out the liquid after about 3 days and boil the liquid again then pour it back into the jar.

Repeat this process every 3 days for the grand total of THREE times.

This process helps eliminate any impurities in the jar and prevent spoilage.

REFRIGERATOR PICKLES ARE GREAT BUT HERE ARE SOME THINGS YOU SHOULD KNOW:
“Refrigerator pickles Some pickle recipes that call for enough vinegar (5 percent acetic acid) can be stored safely in the refrigerator at 40° F or colder for up to 1 month. These pickles do not require heat processing, but they must be kept refrigerated. Do not decrease the amount of vinegar in these recipes; an unsafe product may result.”
Cautions about Refrigerator Pickles

find out more >

“For many years, refrigerator pickles have been regarded as very safe. However, as reported by the U.S. Centers for Disease Control and Prevention, recent studies have concluded that Listeria monocytogenes survive and multiply in low-acid, refrigerator pickles for several months. If you are in a high-risk group for food-borne illness, treat refrigerator pickles as fresh food and consume them within 3 days. Otherwise, you should consume only fermented or canned pickles.”

Packing Green Tomato Pickles in November 2020