From Wiktionary, the free dictionary
From uni- + ball + -er, punning on Unabomber.
uniballer (plural uniballers)
- (slang) A man with only one testicle; a monorchid.
2002 March 29, Blarg!, “Tom Green in Japan”, in rec.arts.anime.misc[1] (Usenet):PRAISE BE THE UNIBALLERS!!!/Together we stand/Proud as can be/We unzip our flies/Now see us pee./We're the UNIBALLERS!
2008 November 20, David E. Powell, “Report: Hitler Truly Only Had One Ball -- Bollock Not Bollocks”, in us.military.army[2] (Usenet):Hitler was a Terrorist: The Uniballer.
2009 June 8, Lemon Club rj, “Re: Philly sucks”, in rec.bicycles.racing[3] (Usenet):Agreed - just have a single 156 mile race for everybody - dicks, pussies, uniballers, eunuchs, trannies, whatever.
2011 February 28, Fredmaster of Brainerd, “God damn it's great to have two testicles !”, in rec.bicycles.racing[4] (Usenet):If nothing else, I just learned that Goering really was a uniballer. This if nothing else should be the final straw of evidence against LANCE.