I have worked with automotive AC systems frequently, and have brought the systems in many vintage cars back from the dead. Mobile AC systems can have all sorts of leaks in them that you will probably not encounter with a household refrigeration unit. The refrigerator however is probably using R12, just like mobile AC systems used. This refrigerant can be replaced with R134, since it runs at similar pressures. The problem with R134 is that it will not circulate the mineral oil that was used to lubricate compressors in R12 systems of the past. PAG or Ester oils will need to be used, and the entire refrigeration loop will need to be flushed of all leftover oil before the compressor and refrigerant changeout.
Installing a new compressor in the fridge will involve finding one that is about the same displacement. You can install a modern equivalent from a newer junked fridge if you know the displacement, and output volume of the old compressor... technical information you may have a hard time finding. Once you obtain the new compressor, you will need to cut the old one out. Now the EPA says you need to have the system evacuated to avoid releasing the R12 into the atmosphere, but who's going to know that the line wasn't damaged in transit and it caused the freon to leak out!!! Knowing how to sweat, or solder copper pipe is important in the repair of a refrigerator compressor. You will also need to install some line taps with shrader valves so the system's high side and low sides can be connected to a gauge set. These are easy to find at most HVAC supply shops.
Wire up the compressor. Then, solder in the new compressor lines, the receiver-dryer, and the shrader valve taps, and you're ready to go. The high and low side pressures, and the refrigerant capacity is usually stated somewhere on the fridge's spec plate. Vacuum the system out with a vacuum pump for 1 hour. Let it then sit with a vacuum to ensure you got a good seal. The vacuum should stay there. Then, connect to your can of refrigerant, and charge into the vacuum through the low-side port. Start the compressor up after the refrigerant stops flowing in. The compressor will suck the rest in. Watch the pressures and cut the valves off when the correct pressures are met.
Pick a refrigerant. There are many R12 replacement blends out there. A good idea is to get refrigerant that has an oil charge, or a pressurized can of oil charge. This makes it easy. The amount of refrigerant oil the unit needs should also be stated on the spec plate. R134 may be a little different in high side pressure than the old R12 stuff. Typically in the automotive world, the rule of thumb is you want to charge 2.2 to 2.5 time ambient temperature, for instance if it's 80 degrees, you want to be around 170 to 200 PSI. Don't know if this holds true with refrigerators though.
It's probably a good idea to install a receiver-dryer in the refrigerant loop too after a compressor changeover. This is a small can that costs between $30-50 that contains a dessicant and filters. When a refrigeration loop is opened up, even after vacuuming, there will still be moisture and contaminants in the system that the receiver-drier will remove. This will ensure long-term durability. They are avaliable at most HVAC and refrigeration supply shops.
One thing that you could do to is check into hydrocarbon refrigerants. These refrigerants are a blend of CO2, butane, and propane. HC12 is the equvalent to R12 freon, and will circulate the old mineral oil, so there's no need to flush the system completely. This stuff sounds dangerous to charge a refrigeration system with, but it really isn't for two big reasins. Part of the process of charging a refrigeration system is to evacuate all the system of air. Since there's no air in the system, there's nothing to burn. Also, since there's CO2 in there, it will keep any burning from occuring anyways. The second is the fact there is not any source of ignition within a refrigeration loop that could even cause the stuff to ignite. Hydrocarbon refrigerants have been made illegal in automobiles partly because the EPA has bowed to industry pressure (companies know how cheap and how well the stuff works, and the chemical companies that make CFC's could easily be put out of business!), and because of the off chance the condenser is punctured during a collision, it could result in the release of the flammable gas (R134 is flammable too BTW!) Many Asian built refrigerators however are using hydrocarbon refrigerants with good results. The refrigerants carry more heat, and have lower head pressures. The result is a cooler fridge that uses less electricity!!! I have posted a link here to enviro-safe refrigerants who sells hydrocarbon refrigerant for appliances and automotive uses.
