Green’s Dictionary of Slang

(US) a diluted or even alcohol-free drink, as consumed by a ‘hostess’ who is persuading her client to buy hugely overpriced ‘champagne’ etc.

1890–1904		Farmer & Henley Sl. and Its Analogues.
1928		W. Winchell Your Broadway & Mine 11 Dec. [synd. col.] The women [i.e. club hostesses] are given ‘downs’ by the bartender. A ‘down’ is a Delmonico glass full of ginger ale, but the spender thinks she is drinking likker.
1933		‘William Juniper’ True Drunkard’s Delight 229: Of course, there is small beer or down.
1952		A.J. Liebling ‘So Proud to be Jimmy-jammy’ in Liebling at Home (1982) 191: The girls do not drink ‘downs’, — soft drinks represented to the customers as whiskey.
1960, 1975		Wentworth & Flexner DAS.
1971		Winick & Kinsie Lively Commerce 171: ‘Downs’ enable her to give the customer the impression that she is drinking with him.