In the episode "It's Not Easy Being Green", Global Dynamics needed 'Eureka' sheriff Jack Carter to collect all the samples of globinium (a safe alternative to plutonium) in town. Tess Fontana teased him by saying that he could rely on his easy-going Andy Griffith charm to get those people to give up their samples.
No Zonk here to be deactivated! There's no mention of any of Griffith's TV shows, but we all know which one she meant. I mean, Carter's a small-town sheriff like Andy Taylor; I don't think he's going to be confused with a Southern lawyer or a private school's headmaster.
Luckily for the integrity of the Toobworld structure, we're in the Trueniverse; within the reality of Earth Prime-Time, Tess was just referring to Andy Griffith's charm as a comic story-teller - the guy known for such stories as "What It Was, Was Football".