Since I cited Wheee! Blog as a source of "Say Say My Playmate" versions, it is only fitting that I refer anyone interested to this Mudcat thread

Children's Street Rhymes

One example from that thread was provided on March 11, 1998 by Marc B.

Playmate

Say say my playmate
Come out and play with me
and Bring your dollies three
Climb up my apple tree
Slide down my rainbow
and we'll be playmates forever more.

Enemy

Say say my enemy
Come out and fight with me
And bring your devils three
Climb up my poison tree
Slide down my razor
Slam! into the dungeon door
And we'll be enemies forever more.

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Thanks, Marc!!