The song that Andy sings on the front porch is titled "There Is A Time". It was written by Rodney Dillard and Mitch Jayne of the group The Dillards (better known as the Darlings"!) It was also performed by the Darlings in episode # 139 "The Darling Baby" and sung by Charlene.
(Aunt Bee is getting the guest room ready for cousin Gloria; Andy and Helen are there)
Andy: Anything else I'm supposed to do?
Helen: Oh, Andy, don't be so grumpy.
Aunt Bee: All I did was ask him to make her feel at home.
Andy: I don't understand that.
Andy: People travel hundreds of miles to get away from where they live and when they get there everybody tries to make 'em feel at home. I don't understand that.
Aunt Bee: A philosopher.