When I was a kid, we had a Little Golden Record of 'Playmate,' and I remember the tune well. Recently I got a surprise. I was looking at old parlor songs at the University of Missouri - Kansas City's collection of local music. (It is called the Kansas City Collection.)

Charles L. Johnson was a resident of Kansas City, Kansas, and he published about 300 works, including the well-known rag 'Dill Pickles.' I downloaded a tune he wrote in 1906, called 'Iola' and played it. The chorus of 'Iola' is the tune for 'Playmate.'

It's been fun exploring that collection, but there are problems at present with printing things. They are "changing platforms."
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The old house to the north of me has a cellar door as in the song. I cannot imagine anybody sliding down it, even after a rain. The wood's too rough and there isn't enough incline to get going.

I doubt if any kid ever really did it.