Green’s Dictionary of Slang

drops of liquor that fall onto the careless drinker’s clothing.

c.1698		B.E. Dict. Canting Crew n.p.: Tears of the Tankard Drops of the good Liquor that fall beside.
1721		Penkethman’s Jests 85: An idle Fellow, who generally mourn’d for his Sins in the Tears of the Tankard.
1725		New Canting Dict. [as cit. c.1698].
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: tears of the tankard stains on a waistcoat, supposed to be droppings of liquor.
1809		G. Andrewes Dict. Sl. and Cant.
1811		Lex. Balatronicum.
1821		Flash Dict.
1835		G. Kent Modern Flash Dict.
1848		Flash Dict. in Sinks of London Laid Open.
1862		E. de la Bédollière Londres et les Anglais 318/2: tears of the tankard, [...] taches de bière ou de vin sur un gilet.