The question "What's your poison?" is an informal way of asking someone what they would like to drink. Apparently it has been used in this way since the mid-1800s. I read recently that the word "poison" derives from the Latin word for drink (potio, which also gave us potable). It may be just an interesting coincidence that "poison" is being used with the ancient (harmless) meaning. Is there any evidence of the word being used with the harmless meaning in the centuries between?
Not according to the OED.
In an entry updated in 2006, it lists only two meanings as "literal uses": the ordinary meaning, which is also the oldest (recorded from 1225); and a slightly later, but obsolete, meaning "A drink prepared for a special purpose; a medicinal draught; a potion."
Under "extended uses" it lists "colloquial (originally U.S.). Alcoholic liquor; an alcoholic drink. Frequently in what's your poison?: what drink would you like?" from 1805, but no other uses without deadly connotations.
Poison, as a jocular way to refer to a drink, is from the mid 19th century:
Liquor was jocularly called “poison” in the 19th century. Bar patrons would select their “poison.” “Nominate your poison” was cited in March 1864. “Name your poison” was cited in December 1870. “What’s your poison” was cited in July 1871.
“Choose your poison” and “pick your poison” both appear to have come later. “Choose your poison” has been cited in print since at least 1888 and “pick your poison” since at least 1913. Intoxicating liquor no longer has to be the “poison” of the subject. An 1888 “choose your poison” citation referred to Democrats and Republicans.
"What's your poison?" is an ironic reference to the aim and slogans of the Temperance Movement - a social movement that was strongly opposed to the sale and consumption every form of alcoholic drink - which described alcoholic drinks as poison.
From "The Ipswich Series of Temperance Tracts. Nos. 1-349" (1917)
“But dram drinkers should notice another thing. The alcoholic beverages of commerce are even worse than the alcohol itself. They do not get the alcoholic poison pure; but it is further drugged with still other poisons. Read a part of the catalogue of agents in common use, namely ; Essential Oils, Cocculus Indicus, Logwood, Brazil Wood, Alum, Green Vitriol. Oil of Vitriol….”