The town was "stress-free" because the only married man was Otis, and he was a drunk! WRONG.
This is another statement I see people make on Facebook on regular basis, but it is completely wrong. Yes, Otis is the "town drunk," and yes he is married while Andy, Barney and several other prominent characters are not, but there are plenty of married couples in Mayberry. I mean, come on, if there were no married couples, where did all the kids come from?
1. Mayor Pike - This was the first Mayor shown on the show. Unfortunately the actor who played Mayor Pike died in 1961 so he was replaced by Mayor Stoner at the start of season 3. We know Mayor Pike is married because in S1E13 ("Mayberry Goes To Hollywood") his teenage daughter Juanita is forced to sing for the movie scouts, and in S1E16 ("The Beauty Contest"), the Mayor talks about his wife riding out on a horse and singing opera during the annual Mayberry Founders's Day Celebration.
2. Mayor Stoner (Played by Parley Baer) - This is the second character to be shown as the Mayor of Mayberry, and he doesn't get along with Andy. In S3E12 ("The Bed Jacket"), it's Aunt Bee's birthday, and she wants a "bed jacket" that she saw in a store window. Unfortunately it was the last one, and Mayor Stoner has already bought it for his wife.