Unbelievable! I had no idea this song was so widespread. This was sung to me by my grandmother. In turn, I sing it to my kids. It's one of their favorite lullabies. The lyrics I learned go like this:

My pigeon house I open wide
And set all the pigeons free.
They fly from their house in the merriest glee
And light on the tallest tree.

And when they return from their merry, merry flight,
They close the doors and say goodnight.

Coo-roo, coo-roo, coo-roo, coo-roo, coo-roo, coo-roo, coo-roo.