The Online 78rpm Discographical Project lists 3 recordings of CONVERSATION WITH A MULE:

Artie Hall's Radio Rubes, Melotone 7-12-54, 1937.

The Roaming Philosopher, Musicraft 566. No date, but it looks like it would have been in the late 1940s.

Arthur Smith, MGM 10791. No date, but it looks like 1950.

"How Can I Keep from Singing," David King Dunaway's biography of Pete Seeger, says his CONVERSATION WITH A MULE was released in 1949.