I -think- all diesel powered refers would be vastly too big for typical homestead use, unless you need a walk in cooler.
Propane units from a truck would also have a compressor, and would also be much too big of capacity for typical refrigerator use. Look up the fuel usage numbers for a typical truck unit--it's a big number.
But there are also absorption type refrigerators that have only an adjustable flame, and no other moving parts. Here's an example of an absorption refrigerator:
https://www.lehmans.com/p-3505-dometic-kerosene-refrigerator.aspx?show=all
RV's often come with the propane fired absorption refrigerators AND an electrically driven compressor so you can run off either fuel. You might be able to get one cheap through a salvage place.
Dometic is pretty much the benchmark against which all others are measured. The amish use them a fair amount.
Most if not all of the absorption refrigerator units use ammonia as the refrigerant. It's way way way more toxic than the "freon" based conventional refrigerants. Leaking ammonia refrigerant can kill you. The domestic sized units have such a small amount, I wouldn't be overly worried about that, but it is a meaningful difference.
How big of a refer do you need???
troy