Good question. (Probably because too many Yanks are teetotalitarians. But good on Alabama; we don’t have any official provincial beverages, period, here in Canada – though I’d rather have none than milk or water, like so many U.S. states have boringly chosen as their official state beverages.)
As it turns out, only one state—Alabama—has stepped up to the bar, choosing Conecuh Ridge Whiskey (a recreation of a Prohibition-era aged moonshine) as its official beverage in 2004. (Amusingly, the owner was subsequently busted for liquor law violations, and the whiskey is now sold under the name Clyde May’s Conecuh Ridge Whiskey).