Green’s Dictionary of Slang

(orig. UK) a euph. for drunk.

1825		C.M. Westmacott Eng. Spy I 392: In would roll three or four jolly fellows, claret-cosey, and in three minutes put it all into uproar again.
1828		R.M. Bird City Looking Glass V ii: Drink you porpoise. If you should become cosey, I’ll send to the ’pothecary for sal aeratis.
a.1856		B. Franklin q. in Hall 1856 461: Dr. Franklin, in speaking of the intemperate drinker, says, he will never, or seldom, allow that he is drunk; he may be ‘boosy, cosey [...] is a little feverish, pretty well entered, &c., but never drunk’.