The oil in an R12 system such as yours is always Mineral oil.
The 124 MB is one of the very worst candidates for conversion to R134. Why are you wanting to convert? If you have a leak, it would be simpler and much less expensive to simply repair the leak, evacuate and recharge.
If you insist on converting, the entire system needs to be dismantled, the system thoroughly flushed to remove old oil, 134 compatible o-rings used with nylog sealant, the compressor removed, emptied and oil flushed with Ester oil, put in correct amount of ester oil, conversion fittings installed, new filter drier, evacuated and charged with 80% of the original volume with 134. If you want it to have a chance to cool well in stop and go traffic, you should also throw out the original serpentine condensor and replace with a parallel flow.
Some will tell you to get a conversion kit from Wal Mart. These are called Death Kits by many for good reason. Your a/c would last a short time should you take this approach.
R12 is coming down in price. Repair your leak, charge with R12 and you will be money ahead, as well as have an a/c that will actually keep you cool.