Green’s Dictionary of Slang

(Aus.) a generator.

1968		D. O’Grady A Bottle of Sandwiches 187: ‘What’s the matter, Jock? Crocodiles?’ ‘Genny, I think,’ Jock said. [...] ‘Gena-bloody-rator. Smells like she’s playin’ up.’.
2012		W. Keyser ‘Carny Lingo’ in http://goodmagic.com 🌐 Genny (pronounced ‘jenny’) — The generator truck.