Green’s Dictionary of Slang

(Aus./US) mildly drunk, tipsy.

1845		J.J. Hooper Adventures of Captain Simon Suggs (1851) 44: Ask him if he didn’t drop a couple of hundreds at the Big Council? Certainly — but then he was ‘drinky and played careless’.
1880		Western Gaz. 12 Nov. 6/1: He had a ‘palatic’ stroke [...] He was very drinkey.
1901		Bulletin (Sydney) 12 Oct. 13/3: Also, the theatre-door loungers who bulk largely in the alleged detective force made little effort [...], contenting themselves with waiting until some furiously jealous or drinky woman should give the venturesome couple away.
1902		Bulletin (Sydney) 4 Oct. 13/3: No evidence was brought to show why the applicant’s drinky friend, away back in 1895, thus rushed a drinky mate into marriage.
1908		N.Z. Truth 22 Feb. 2/3: His drinky nibs [...] used the most filthy language.