Who sings the children's song-Feet up, pat them on the po po?

I think you are thinking of the song called...

Feet Up (Pat Him On the Po-Po)
Guy Mitchell
Written by Bob Merrill

Feet up, pat him on the po-po
Let's hear him laugh Ha-ha!
Feet up, pat him on the po-po
Let's hear him laugh
Ain't seen a babe like this before
He's so good-lookin', going to have some more
Feet up, pat him on the po-po
Let's hear him laugh

Ha-ha now I've been known to gamble, take a little drink
Then there's the night I had a fight and landed in the clink
But now my rootin' tootin' days are done
Got to be the man that he thinks I am 'cause I love my son

Ha-ha I knew a lotta women when I was on the go
They'd stand in line to drink my wine and help me spend my dough
But my wife Rosie ain't that kind
Got her to thank for a buck in the bank 'n' this kid of mine

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There is also an old Australian nursery rhyme that has those words I believe. The Aussie's can help you with that one if this is not the song you were thinking of.