Green’s Dictionary of Slang

(US) tiny.

1916		J.G. Cruickshank Black Talk 43: Dem peeny li’l boy an’ all gi’e rudeness.
1970		F. Collymore Notes for Gloss. of Barbadian Dial. 85: Peeny, pinny. Tiny. Also peeny-weeny.
1974		(con. 1945) E. Thompson Tattoo (1977) 293: Tompkins had such a peeny pecker he’d of had to lope it with forefinger and thumb.