It's worth adding the following to the list from the Ballad Index:

Fontana        LP STL5432. Hedy West
Folkways LP FA 2363 Roscoe Holcomb
Rounder        CD 1011 The Bray Brothers with Red Cravens
Yazoo CD 2200 PETE STEELE
Smithsonian Folkways        SF CD 40077 Willie Chapman
Heritage LP 18 Roscoe Holcomb                
County LP 717 Gaither Carlton        
Rebel CD Reb-4000 Red Allen/Frank Wakefield                
County LP 757 Glen Smith                                                                                                        
The John Hammond track is available on The CD, Music of Kentucky: Early American Rural Classics 1927 - 37: Vol 2. Yazoo 2014.
The Coon Creek Girls' version was reissued on Trikont US-0310, Flowers in the Wildwood: Women in Early Country Music.

Finally, one of Stefan Grossman's videos of old time music at the Newport Folk Festival has some very impressive footage of the Coon Creek Girls performing Little Birdie.