I've been looking for a while since my only sightings of it in the past were on the Left Coast. Just a few days ago I picked up some in a WalMart in Hiram, Georgia...my own back yard. Although only found in cans, I was still pleased to find it. I suspect it is distributed by a unit of Buffalo Rock, but I have not confirmed that as of yet.
I've found Green River 6-pack cans in Super Target stores before. It's a shame, because those Super Targets usually have a great selection of bottled old style sodas, like Virgil's Root Beer, Southern Swirl, etc. They even carry Jones drinks. But they only have Green River in cans. The bottles tend to taste better.