If only I could type:

Although this is a rather old thread, some sources might be useful.

Shown in: American Ballads, Naughty Ribald and Classic, Presented by the Editors of Gold Medal Books (A Red Seal Book), Compiled by Charles O'Brien Kennedy with the Assistance of David Jordan, Fawcett Publications, Inc., New York, First Edition, November 1952.

The Piddling Pup (A Tale of a Pedigreed Piddlin' Pup in Ten Piddles and a Puddle)

With a subhead:

"I have often wondered, when observing George Jean Nathan, the dean of American Drama Critics, walking his dog on 44th street, if he applies the same critical standards to its performance as he does to ordinary dogs."

The verses, which are as posted by Earl above, are each separately titled "Piddle No. 1," "Piddle No. 2," through "Piddle No. 10." Piddle No. 10 is shortened to 4 lines, with the final "The city dogs conventions held…" labelled "The Puddle."

Attributed to "Unknown."

(The Nathan Award is administered by the Cornell University Department of English, under the terms of a trust established by George Jean Nathan (1882-1958), author and critic, who graduated from Cornell in 1904)

Note that this recitative does not appear in Kennedy's A Treasury of American Ballads, Gay Naughty and Classic published McBride Co., NY, 1954.

Also appears in Songs for Swingin' Housemothers, Frank Lynn, Chandler Publishing Co., San Francisco, 1961, as "Rex, The Piddling Pup." Text is as posted above. No attribution – presumedly it's that guy "Anon Amos" again. A melody line and chords are given here.

Appears in A Book of Vulgar Verse: An anthology of ballads, sailor's songs, cowboy songs, college songs, parodies, limericks, and other humorous verses and doggerel now for the first time brought together in book form by "A Gentleman About Town," Checkerbooks, Inc., Toronto, ISBN 0-89009-411-X, December 1981, as "The Diabetic Dog."

First verse here is:

A famer's dog came into town,
His christian name was Runt.
A noble pedigree had he,
Nobless oblige his stunt.

Remaining verses as posted previously.

Again attributed to "Anonymous."

John