Hmmmm. It's in a book called An Alabama Songbook: Ballads, Songs, and Spirituals. Unfortunately, I don't have that one. HOWEVER it's also in a book called Songs of Man (The International Book of Folk Songs), by Norman Luboff and Win Stracke (1965). From this book, I get the impression that the song is Win Stracke's English version of the German "Muss I Denn" - could that be?

Here are the words from Luboff/Stracke:

My Pigeon House
(tune: Muss I Denn)

My pigeon house I open wide
And I set my pigeons free.
They fly up high, up to the sky,
And they sit on the highest tree.
And when they return from their merry merry flight,
They shut their eyes and they say, 'Good night!'
Coo-roo, coo-roo, coo-roo, coo-roo,
Coo-roo, coo-roo, coo-roo.