Green’s Dictionary of Slang

smile n.1

also fancy smile
[i.e. it promotes a smile or one’s lips open in a ‘smile’ as one drinks]

(orig. US) a drink, usu. of whisky, esp. in phr. take a smile.

[US]Spirit of the Times (NY) 24 Aug. 294/3: We all agreed to take another ‘smile’ [DA].
[UK]‘Epistle from Joe Muggins’s Dog’ in Era (London) 16 July 3/2: [W]e dropt into Jones’s, opposite the Admirality, as the Yankees say, to ‘take a private smile’ at the bar.
[US] Poem before the Iadma of Harvard College in Hall (1856) 7: Hast ta’en a ‘smile’ at Brigham’s.
Border Sentinel (Mound City, KS) 12 Jan. 3/1: Took another smile of lightning and went home.
[US] ‘English Sl.’ in Eve. Telegram (NY) 9 Dec. 1/5: Let us present a few specimens:– [...] ‘Let’s take a smile.’.
[UK]M. Roberts Western Avernus (1924) 109: ‘Come, step up, boys, what’s your liquor?’ ‘Take a smile.’.
[Aus]Dead Bird (Sydney) 12 July 5/4: Boss’s Barometer [...] A.M. 9 o’clock A Morning Smile.
[UK]Mirror of Life 20 Jan. 7/4: A bitter smile — Whisky and bitters.
[US]W.C. Gore Student Sl. in Cohen (1997) 22: smile [...] 2. n. A drink.
[US]Independent (Honolulu) 3 Oct. 1/2: Take a smile [...] ‘Take a little wine for they stomach sake’.
[US]T.J. Carey Hebrew Yarns and Dialect Humor 81/1: The slang of our day is a puzzle, / Invented by — ah, who can tell? / A drink is a ‘smile,’ or a ‘guzzle,’ / A swindler is merely a ‘sell.’.
[Aus]Sydney Sportsman (Surry Hills, NSW) 23 Jan. 4/2: If he serves a ‘smile’ on Sunday, the vigilant and outraged bearer of the blue livery of the law swiftly sumonses the publican for this peccadillo.
Wash. Bee (DC) 20 May 4/6: He asked me to take another ‘smile’ and a straight ten-cent cigar.
[US]L. Axley ‘“Drunk” Again’ in AS IV:6 441: Once I received an invitation to take a drink by means of the rather euphemistic question, ‘What about a little smile?’.
[UK]‘William Juniper’ True Drunkard’s Delight 228: You may have a [...] smile, or fancy smile.
P. Grey ‘’Twixt Night ’n’ Dawn’ in Afro-American (Baltimore, MD) 3 Dec. 11/5: That quiet, comfy homelike atmosphere in which to enjoy a ‘light smile’.
Beebe & Clegg US West 302: It is no task for the imagining [...] to pass the hospitable doors of Barry and Patten’s in Montgomery Street for a ‘smile’ at the invitation of the Emperor Norton [DA].

In phrases

do a smile (v.)

to take a glass of whisky, or any other drink.

O. Harrison Comic Guide to Isle of Man 98: ‘Who can’t do a smile?’ asked a grinning tourist, producing a pocket-flask.
[UK]J. Ware Passing Eng. of the Victorian Era 111/2: Do a smile (Amer., 1860 on). To take a drink. Now rarely heard.
will you try a smile?

an invitation to drink.

[UK]Barrère & Leland Dict. of Sl., Jargon and Cant.
[UK]Morn. Post (London) 18 Feb. 2/3: American invitations to drink [...] ‘Will you try a smile?’.
Y.P. Kazakov Autumn in the Oak Woods 152: ‘Will you try a smile, dad?’ he said, slapping the violinist’s fat back. ‘Vivace adagio, eh? Ha-ha! Come on, drink to the sailors’ health.’.