I have a few fragments of my family's version.

Looking through the keyhole
At Father's wooden leg
Oh, why did they put the shore so near the ocean,
the ocean?
Go get the flit, there's a fly in Grandpa's soup.

Horses running 'round
Their feet are on the ground
Oh, who will wind the clock when I'm away,
away?
Go get the listerine, sister wants a beau.

...

We feed our baby garlic so we'll find him in the dark.

...

Go get the axe -- here comes the man from the income tax!

[I bet dollars to doughnuts my second cousin made up that line.]