If you simply google strings like droppin' g's, droppin' my g's, droppin' some g's, etc., you get lots of hip-hop lyrics from these to Eminem. Mostly it's about droppin' and 'G' of a different sort.
Linguistic g-droppin', as Language Log's Mark Liberman laid out a while back here, involves no direct 'dropping' of anything, just a difference in where you put your tongue – 'ng' like in sing has it at the back of the mouth (velar) while 'n' like in sin has it at the front (at or near the alveolar ridge).
Mrs. Verb found the cartoon here in a really old New Yorker. It has a whiff of Bush about it – as a boy with deep roots in superrich WASPy Yankeedom doing hyperdialectal Texas – but it really strikes me as getting nicely at a popular notion of styleshifting.