It occurred to me that—if "sink" = "empty [a drink]"—a search for "sink a pint" might yield early matches—and it did. Examples of "sink a pint" as (evidently) a familiar slang term in Australia go back to at least 1896, with a rather inconclusive first occurrence in a very brief rumination from "They Say," in the Coburg [Victoria] Leader (February 22, 1896):
Could Quack sink a pint.
From "The Bungarra Club," in the [Adelaide, South Australia] Mail (June 8, 1912):
At the recent Conference of Licensed Victuallers it was pretty plain that the abolition of the universal free 11 o'clock lunch was favoured. He [the club president, Mr. Wiggleswick] was by no means in favour of such abolition. (Cheers[.] Voice—"That's all you live on.") The man who interjected was not truthful. (Applause. Voice—"Chuck 'im hout.") To prove it, he would say that he had only just dined with a friend. ("WE know that.") He never used counter lunches himself.—(Incredulous murmurs. Voice—"You ken tell 'em all right')— but he wanted to see them retained for the benefit of his many acquaintances who did. (Voice—"Saw you sink a pint and a plate o' sandwidges to-day.") The President—"That is incorrect. I have a twin brother, who is very like me. in fact, he was born at the same time. (Delirious mirth.)
From "Town Topics and Tit-bits" in the Jerilderie [New South Wales] Herald and Urana Advertiser (April 10, 1914):
Give us beer! oh Lor! Give us beer! / Oh! dash the water famine—that's nil gammon! / We don't drink water (though they say we ought 'er) / It's got no sting—won't make us sing— / Why strike me pink, I'd sooner sink / A pint of beer—glorious beer!
From "Schoolmaster Cited for Libel: Greghamstown Farmer the Plaintiff," in the [Orange, New South Wales] Leader (February 11, 1916):
"Dear Dad. I have noticed letters in the local papers where you have made a fool of yourself on more than one occasion. I would give a man in your position the credit of knowing better sense. As far as getting recruits is concerned I think you will do more harm than good. Sinking a pint of beer is more in your line.
And from "The Hum Association," in the Rosedale [Victoria] Courier (July 19, 1917):
He [the president of the Hum Association] had an excellent style of getting a drink. I was at the bar of Kelly's (Cowware) Hotel when in walked the president. "Oh, good day," said he, "you are looking well. It is evident by your appearance you have discovered the elixir of perpetual youth." This was too much for me ; I shouted, and my friend did likewise. It was surprising the velocity with which this "never work" could sink a pint. I also met the secretary, he was no disgrace to the position or his colleagues, for he could hum one with the "best of 'em."
There is also an early instance of "sink a glass" from "St. Patrick's Day," in the Morwell [Victoria] Advertiser (May 6, 1904):
"I'm all right when you know me, / But nasty when I'm vexed; / I can sink a glass of whisky / With any of my sex. / I can ride a colt so easy, / Boss cattle in the scrub, / In the cowshed I'm a daisy, / And a dazzler at a pub."
And an even earlier instance of "sink a cup", from "The Egeria's Cruise to the Hunter Islands," in the Launcestown [Tasmania] Examiner (April 15, 1893):
Our captain, clothed in oilskins and sou'-wester, defies the elements and keeps the Egeria well on her course, and not until the Mersey light had faded from his sight did he leave the wheel to "roustabout," with strict instructions to keep her steady while he retired below to sink a cup of coffee and a biscuit.
