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1.
Often used in high class british porn; when a guy is a complete gentlemen with his genitals. Keeping his pubes well groomed and clean. Also being polite and asking kindly if they could have sex.
(all in british accents)
Male: May I please insert my penis into your vagina.

Female: Oh, what I gentleman!

Male: No my dear, I'm a Genital-men!
by sean_23 December 24, 2010
 
2.
A humorous way of mixing the word genitals and gentlemen when speaking of and to fellow men.

Good evening genitalmen how doth it hang this fine day?
Genitalmen how are you today. I see by your constant tugging on you privates something is amiss!
by dragonneus December 07, 2011