Noun. Newfoundland English for strong alcoholic beverage. (To bung one's eye is to drink heartily.) Usage: "When I was out walking, my sea stock to buy, Got tricked in the liquor, and bought Bung-'er-eye." (Note: usually pronounced "bung your eye" or "bung yer eye.")
From the Dictionary of Newfoundland English, 2nd ed., p. 74.
And let me just say how DELIGHTED I am to finally figure out why there's a fife tune, very popular in the eighteenth century, called "Bung Your Eye." Wahoo!