According to Meade et al.'s Country Music Sources,
[Ref: (2) Gordon Ms., #2409 (contributed ca. 1928)]
The earliest sound recording is:
Beautiful Brown Eyes (BS 01198-1) - Arthur Smith Trio (vcl by Arthur Smith w/vln & 2 gtrs) - 08/03/1937. Charlotte, N.C.
Bb B7221 - 12/1937 MW M7343
~Masato