Green’s Dictionary of Slang

blackbird n.2

[var. on bird n.3 (1); there is no racial implication]

(US) the penis.

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[US] in Randolph & Legman Ozark Folksongs and Folklore (1992) I 97: Well, I took her ’round the waist an’ I gently laid her down [...] While the blackbird and the thrush were a banging in the brush, / I wound up her little ball of yarn, yarn, yarn.
[US]Botkin A Treasury of Amer. Folklore 809: Fair maid, pretty maid, / Give your hand to me, / I’ll show you a blackbird, / A blackbird on the tree.
[US]Randolph & Legman Ozark Folksongs and Folklore I 97: The blackbird is the penis, and the thrush is the woman’s downy pubis.

In compounds

blackbird nest (n.)

the vagina.

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[US] in E. Cray Erotic Muse (1992) 287: You put your hand beneath my dress, / And there you found a blackbird nest.