In general in the U.S., the cutoff date for public domain is 1923 - material from 1923 and earlier is quite surely in the public domain. Everything after that was affected by the Sonny Bono copyright extension of 1998, so mostly you're out of luck with recordings made after 1923 - the first Carter Family recordings were 1927.
It's different in the UK - I think some Carter recordings have come into the public domain there.

-Joe-