You used to be able to get these for your house. My father told me they were common in places were gas was already installed but not electricity. They made a "pop, pop, pop" sound when running.
I got a propane fridge and it's totally silent which is one of the reasons I got it, besides being off-grid..
it's 18 cubic feet and I have to keep it at it's 'warmest' settting in this 80F weather.. it's a "Crystal Cold" made by the Amish..(no light inside!) (though it does have a piezo igniter, go figure)
My parents had a Servel Electrolux gas refrigerator in the kitchen when I was a kid. It didn't pop. It was very quiet. I think it was purchased around 1940.
ditto on that. I am thinking of getting a 8 cubic foot one to be the second fridge. I would like the option where it can run on AC/DC or propane. Already have a 100 # gas tank for other uses.
I'm guessing some of the RV fridges outlive their RV's so you might be able to pick one up for a few bucks. Would seem to be worth a try before you drop big bucks on a larger one.
The ones I've had in both my truck campers have been Norcold 3/way. They will get real cold real fast on propane. But they must have good circulation thru the condensing coils. The venting and circulation for the fridge is not that great in my current camper (Starcraft) so I've installed a 12v muffin fan (very low draw) that will also run fairly well on a small solar cell. Makes a big difference.
Don't remember the brand but my friends dad is a plumber and one of his friends had also aquired one of these units. It was a very old one but it still works.
Anyway, they moved it into his garage and he plumbed it with gas. Now it keeps his beer and extra food cool without using any electricity