The Online 78-rpm Discography Project lists these recordings:

DEAR OLD PAL OF YESTERDAY
Arthur Fields 1927?

MY PAL OF YESTERDAY
Bill Bruner 1929

MY OLD PAL OF YESTERDAY
Jimmy Long 12/1/30
Joe Lester (Jimmy Long) 12/1/30
Gene Autry & Jimmy Long 10/30/1931
Gene Autry 10/30/31
Long Bros, 10/30/31
Joe Lester & Dick Moss (Long), 1929-31?
Judie and Julie 08/??/39
Buddy Starcher, 1950?

OLD PAL OF YESTERDAY
Girls Of The Golden West 1933

AT TWILIGHT, OLD PAL OF YESTERDAY
Ramblin Duet 1937

In addition, there are a couple of recent CDs that feature the Carter Family, but I presume these were taken from radio broadcasts, and were not released as singles.

Allmusic.com lists additional recordings, all presumably more recent, by Norman Blake, Amy Gallatin, Jerry Lee Lewis, Cliff Perry, Red Smiley, and Jody Stecher.