We used to do this one - it had a pretty elaborate clapping schematic, which I only remember parts of... I guess it's true - the mind is the first to go.

Say say oh playmate
Come out and play with me
And bring your dollies three
Climb up my apple tree
Slide down my {rainbow? rain barrel?}
Into my cellar door
And we'll be jolly friends
Forever more, more, three four.

There was a "Say say oh enemy" revision that was my first real introduction to the concept of parody, but I don't remember the words...