Why did Atticus put a Cunningham on the jury?

Atticus put a Cunningham on the jury because he knew that they were fair-minded.  

The jury is made up of farmers, and the Cunninghams are farmers.  This is one of the reasons why there is a Cunningham on the jury.  Scout recognizes him from the lynch mob who tried to attack Tom Robinson before the trial even started. 

The jury sat to the left, under long windows. Sunburned, lanky, they seemed to be all farmers, but this was natural: townfolk rarely sat on juries, they were either struck or excused. One or two of the jury looked vaguely like dressed-up Cunninghams. (Ch. 16)

Jem is surprised to learn that Atticus would put a Cunningham on the jury after they threatened him and tried to kill his client.  He doesn’t understand that when Atticus stared down the mob, he accomplished more than making them go away.  He gained their respect.  Atticus also understood the way the Cunninghams’ minds worked.

He said the Cunninghams hadn’t taken anything from or off of anybody since they migrated to the New World. He said the other thing about them was, once you earned their respect they were for you tooth and nail. Atticus said he had a feeling, nothing more than a suspicion, that they left the jail that night with considerable respect for the Finches.  (Ch. 23) 

Atticus tells the children that if there had been two Cunninghams on the jury, he would have had a hung jury.  That would mean no verdict.  He said it took “a thunderbolt plus another Cunningham to make one of them change his mind,” but in this case he got close. 

Although it may seem like Scout, Jem, and Atticus are painting all of the Cunninghams with one brush, Atticus is actually being very respectful of them.  He believes that the man he put on the jury was open-minded, and that it is a family trait.  As he showed with Walter earlier, Atticus respects farmers in general and Cunninghams in particular.