What TV show depicts a bearded guy in overalls with aviator glasses and a beardless guy with a stocking cap and aviator glasses?

The TV show you're referring to is likely "Duck Dynasty." It features the Robertson family, known for their bearded patriarch Phil Robertson, who often wears overalls and aviator glasses. The other character you mentioned could be Jase Robertson, who commonly sports a stocking cap and similar aviator glasses. The show follows their lives running a duck call business and their family dynamics.