Green Acres & Petticoat Junction are not set in "The South", they're more of a general rural setting, somewhere in the Midwest. IIRC, Chicago was the nearest big city.
A TV show with some good southern accents is Designing Women. Dixie Carter, Annie Potts & Delta Burke are all genuine southerners.
I grew up in California, but I spent a lot of summers with my father's parents who were from Louisiana. I lived in Connecticut for several years, and listened to Prairie Home Companion a lot. So people are always making wildly inaccurate guesses about where I'm from.
One more thing: For an authentic Loo-siyana accent try Justin Wilson, the Cajun Cook.