Alternate version from my wife who learned it at camp (where else):

Baby Owlet, poor little owlet,
Singing as the night wind blows.
Baby Owlet, poor little owlet,
Singing as the night wind blows,
Singing coo coo coo coo coo,
Singing coo coo coo coo coo,
Singing coo coo coo coo coo,
Baby Owlet, poor little Owlet,
He's crying so.

The tune is ineffably sad.

Bob Coltman