Green’s Dictionary of Slang

1. the vagina.

1798		‘The Blue Vein’ in Hilaria 64: Drink c—t, the blue vein, wherein floods of joy flow.
1835		‘The Blue Vein’ in Fanny Hill’s Bang-Up Reciter in Spedding & Watt (eds) Bawdy Songbooks (2011) III 318: When she pull’d up her clothes, Ned exclaimed, ‘I declare, / Your blue vein I can’t see, ’tis so covered with hair!’.

2. (Aus. prison/N.Z.) the penis.

1835		‘The Blue Vein’ in Fanny Hill’s Bang-up Reciter 26: Ned pull’d up his clothes, sir, when to their surprise, / They beheld his blue vein of a wonderful size.
1990		Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Blue vein. Penis.
2003		McGill Reed Dict. of N.Z. Sl. 27: blue veiner/blue vein flute. The penis ANZ.

3. (also blue veiner) an erection.

1975		J. Wambaugh Choirboys (1976) 36: Roscoe was unable to raise [...] a ‘diamond cutter’ or even a ‘blue veiner’ due to shooting pains in his groin.
1977		G.F. Newman A Prisoner’s Tale 21: He [...] glanced down at his crotch. ‘I’m getting a blue vein here, Ginge,’ he said invitingly to the trusty.
1998		D. Jenkins Rude Behavior 33: ‘This hard-on showed up, Claude. It was a big-time bulb, a fucking blue veiner, man’.