A number of manufacturer's make portable, gas absorption 12V/DC refrigerator/freezers, and one company makes a portable 3-way refrigerator (12V/120V/LP), but all are well over $300. The most affordable, and coincidentally, the only one that can run off propane is the Dometic RC4000 portable refrigerator at around $450-500. ARB, Engel, Dometic and Norcold make units that run off 12V/DC, with prices starting at $480. If you can find one, Engel made a 14-Quart unit called the MRFD-015 which, until it was discontinued, sold for around $350.
A gas absorption refrigerator/freezer will maintain a certain, user-adjustable temperature, usually including below freezing. The cheaper refrigerators use thermoelectric chip cooling, and are not designed/capable of freezing or maintaining a fixed temperature.
I've owned an Engel MRFD-015 refrigerator/freezer for several years and find it very convenient for car camping. I use it as a freezer to store our meats, fish and poultry, and to also re-freeze our ice packs for a standard cooler. The only concern is you need a heavy-duty battery and need to recharge it every day or two. The refrigerator draws about 3.4 Amps at 12V/DC, but runs at about a 30% duty cycle, so it's total power budget is about 24.5AH/day. I've upgraded my Jeep's battery with an Odyssey-brand and find if I let the engine run about an hour every two days, that's enough to keep the battery from going flat with the refrigerator hooked-up. Or you could use a marine deep cycle battery and recharge it via your generator, or even via a solar panel (50+ Watts minimum 6 hours direct sunlight per day).
The Dometic RC4000 has a similar power requirements but can also be run on 16-oz disposable canisters or bulk propane tanks. This unit is also more than twice the capacity of the Engel unit I have (33 vs 14 quart capacity) and is similar in capacity to electric-only units costing more. If I needed to buy a new portable refrigerator today I would give this unit serious consideration.
Remember that a unit like this is a multi-purpose device. My Engel is almost always strapped in the back of my Jeep, set for refrigerator setting, and full of water and snacks. This way if I get stuck on the road or delayed by traffic I have nice cool drinks and food. I use it when fishing, out at the beach and hunting as well as camping. If there's an extended power failure (and my generator gives out) I can freeze 2-Liter soda bottles refilled with water to keep the inside of my refrigerator cool, helping to avoid spoiled food.