I think there is a parity error in my memory but here are the bits I can recover of Piddlin Pete.

Perhaps someone could complete the doggerel

PIDDLIN' PETE

As he wondered down the roadway
Twas beautiful to see
His work on every gatepost
His work on every tree

...................

He piddled on the carrots
He piddled on the ham
And when the grocer chucked him out
He piddled on the jam

(a competition was held among all the dogs and when they were all exhausted i.e "When other dogs raised legs in bluff To piddle in the sky")

Then Pete an exhibition gave
Of all the ways to piddle
With fancy flips and double drips
And then a little dribble

The city dogs said so long Pete
At piddlin' you defeat us
(And then the punch lines !)

Paddy