Parallel Anthology Track 62
No image of record label available. Neither Anthology booklet assigns authorship, nor does www.78discography.com.
According to the Old Weird America blog:
“Sugar Babe” belongs to a family of “rounder” songs, cultivated especially by young men, carefree and assertive in spirit, often risqué and in the Appalachian South associated in the early part of the last century with the five-string banjo. Afro-american influences show up frequently in the “rounder” songs and it is possible that “Sugar Babe” itslef has afro-american connections. [...] Sugar Baby or Red Rocking Chair is a widespread folk song, found in the repertoire of a lot banjo players in the South, and still very popular today with old-time and folk musicians.
There are good grounds for treating this composition as public domain.
Sugar Baby by Paul Clayton album released in 1957 (according to folkways.si.edu): Spotify According to liner notes, "Clayton collected this version from Finlay Adams of Big Laurel Virginia". No arrangement credit claimed.
Red Rocking Chair by Charlie Monroe & his Kentucky Pardners recorded in 1949 (according to RFSD): YouTube Unable to determine whether any authorship or arrangement credit is claimed for this version.
Red Rocking Chair by the New Lost City Ramblers recorded in 1961 (according to www.folkways.si.edu): Spotify Liner notes for this album refer to previous Charlie Monroe version (above) as source.