The lack of CMP carbines probably has more to do with the lack of carbines in the Army supply inventory rather than conversion to full auto issues. To convert an M-1 to an M-2 simply requires the necessary fire control parts, just like converting and AR-15 to an M-16 (more or less).
Need to remember we shipped millions of carbines overseas as foriegn aid. Total production was just short of 6,000,000, which included about 500,000 M-2's. Based on the numbers in Ezell's book, we shipped at least 4,000,000 of those overseas. Just under a million went to South Vietnam. Throw in the carbines sold via NRA/DCM in the early sixties plus normal attrition and I think you come up with the answer as to why no CMP carbines. There just ain't any. Possibly CMP could stumble across a stash overseas like they did with the Danish Garands, but so far no luck.