R152a (commonly found in duster cans) has been used as an alternative to R134a that has about 1/10 the GWP and slightly higher efficiency for A/C applications.
R600a is OK for above zero refrigeration but not very good for below zero. R290 and R1270 (and mixtures containing them such as R433b) do well to -40 or so, and R410a will go below -60 pretty easily.
Not sure how old the refrigerator in question is, but if it's really old, it could be using R40 or R717, both of which are flammable (especially the first) and very toxic. (Some used R764, although that's not flammable, just highly toxic.) After that, it's pretty much all R12, R22, or R134a. Refrigerators using R600a, R290, or R1270 haven't shown up until recently.