I also don't think it's a stretch for the children's song "Playmate" to be added to this thread. After all, it includes the line "Slide down my cellar door".

There's a number of versions of Playmate on this Mudcat thread:
thread.cfm?threadid=8560#53707

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This song is often used as a children's handclap rhyme.

Here's some contemporary versions of Playmate that I had posted on that Mudcat thread:

thread.cfm?threadid=8560#1929063

For those who are still on dial-up connection, here's one example from that post:

Cee Cee my playmate,
come out and play with me
and bring your dollies three,
climb up my apple tree.
Slide down my rainbow
into my cellar door
and we'll be jolly friends
forever more more, shut the door!
-mulfig on May 29, 1999
http://streetplay.com/discus/ ; Discussion: Girl Games: Clap & rhyme; Archive through June 8, 2000