Green’s Dictionary of Slang

sleepy adj.2

(US) a euph. for drunk.

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[US]Burlington Sentinel in Hall (1856) 461: We give a list of a few of the various words and phrases which have been in use, at one time or another, to signify some stage of inebriation: [...] sleepy.

SE in slang uses

In compounds

sleepy dust (n.)

some form of sleeping draught, used to help in robberies.

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[UK]Annual Register 189/2: Probably the watchman was inveigled from his beat at the time the property was removed, or had what is called ‘sleepy dust’ thrown in his eyes.
sleepytime gal (n.) [SAmE sleepytime, bedtime]

(US) a promiscuous woman, a man’s mistress.

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J. Bajer Sleepy-time gal 🎵 Sleepy-time gal, you’re turning night into day. / Sleepy-time gal, you’ve danced the evening away.
[US]R. Chandler Long Good-Bye 293: On account of some lacquered chippie said we used loaded dice. Seems like the bim was one of his sleepy time gals. I had her put out of the club – with every dime she brought in with her.