I haven't found a definitive rendition of the song earlier than yours from 1892 yet, but I have seen evidence that a song it's based upon was around in 1875. Three joke stories in papers from 1875-78 have the following (or a similar) story:

"I'll holler!" she said, clutching the railing.
"You mean that you will scream?"
"Yes, sah."
"And raise a row?"
"Yes, sah."
"Well you just try it on, and if I don't put a sticking plaster over your mouth I'm no Court!"
She looked.
He looked.
And she didn't dare do it.
When the Maria rolled away the boys sang:
  We've traveled this wide world all over,
  And had piles of sorrow and sport;
  But we never laid eyes on a human
  Who'd successfully bluff this 'ere court."

I feel that those lines scan fairly well to the SoA tune but they could also of course come from a different song.

Source (Rochester [NY] Democrat and Chronicle, May 6th, 1875, p. 3) and similar (Daily State Gazette [Green Bay, WI], May 10th, 1875, p. 1; Columbus [Nebraska] Era, September 14th, 1878, p. 5).

Another possible predecessor of the song appeared in 1891 in The Arkansas Democrat (October 29th, 1891) which brings me to a point I've been thinking about: all this time, people have merely mentioned an Irish origin of the song but nothing more. Is it possible the song is Old Rosin the Bow? This song is like a dreary antonym to Rosin the Bow, which would perhaps have made the song more comedic in its day.