early 14c., "den, cave, gollow nook," from Old English cofa "small chamber, cell," from Proto-Germanic *kubon (compare Old High German kubisi "tent, hut," German Koben "pigsty," Old Norse kofi "hut, shed").
Extension of meaning to "small bay, inlet, or creek" is from 1580s, apparently via Scottish dialectal meaning "small hollow place in coastal rocks" (a survival of an Old English secondary sense). Also in early Middle English, "chamber, closet, pantry," hence the legal phrase cove and keie "right of the mistress of a household to control 'pantry and key,'" that is, to manage the household (late 13c.).
"man, person, fellow, chap," canting slang from at least 1560s, said to be from Romany (Gypsy) cova "a thing," covo "that man" [Barrère and Leland].