Hello --
I am a musician and musicologist and a professor at the University of Western Ontario.

I found my self singing this song to my dog this evening, adapting it as "Daddy's little Alabama coon hound" (she's a shepherd-husky-lab mix but looks like she's also a bit coon hound). My mother would sing this lullaby to me in the late 1940s/ early 1950s. She sang it to these words, in a lilting compound duple meter (or swing time):
       La lu_, la lu_, la lu, la lu, la lu_!
       Underneath the southern silvery moon.
       Rock-a-by! hush-a-by!
       Mammy's little baby,
       Mammy's little Alabama Coon.

She might've said Mama's, instead of Mammy's. I don't know where or how she learned it.

She also sang another charming lullaby, in duple time to these words:

Sleepy sparrows in the willows
settle in their leafy nest.
Sleepy children on their pillows
settle for a long night's rest.
Mother bird peeps softly from the branches high.
Little children's mother sings a lullaby.

[at this point she would sing either the Alabama Coon lullaby, or Brahms's Lullaby]

Has anyone heard of the sleepy sparrows song? I've never seen it, nor the Alabama coon one, in sheet music or in a collection before.
Until I did a google search tonight on Alabama coon, I had never seen the lyrics to it.

Thanks.
Dr. Hank (as my universoty music students and colleagues call me)