I had forgotten about this song until I saw that first line posted. My mother knew this one, but my parents have been gone for many years. She probably learned it from listening to the radio, and the 1930's is probably the correct era. She taught me one called "Rythm in My Nursery Rhymes", and they may be from the same time period. I recently found her old high school composition book with page after page of lyrics in it, including "Rythm in My Nursery Rhymes". La Marca's suggestion sounds like the most direct search route. Alice in Montana