Green’s Dictionary of Slang

1. a deaf person.

1856		Life in Boston & N.Y. (Boston, MA) 22 Nov. n.p.: When is deafy Wheeler [...] going to ship old Burns, and live with that curly-headed youth.
1926		L.I. Guiney Letters 193: They are fine seats for a ‘deafy’ like me.

2. (US Und.) a deaf beggar (or one who poses as such).

1937

‘Boxcar Bertha’ Sister of the Road (1975) 301: Beggars [...] may be further sub-divided into groups: a. Blinkey (blind) b. Deafey (deaf) [etc.].