What are the roles of commoners, civilians, or slaves in Coriolanus and King Lear? How are they similar or different? What do they say about Shakespeare's time period?

To answer this assignment, you would want to compare these types of characters and the major characters in the play, to show how the minor/common characters illuminate the nature of the major/noble ones.
Characters to look at in King Lear would include the Old Man who guides Gloucester until he meets Edgar, and the servants in the scene where Cornwall blinds Gloucester, particularly the servant who attacks Cornwall. One might look at the ways in which these characters' moral behavior illuminates that of the major characters.
In Coriolanus, a major role played by the commoners ("plebeians") is to show what kind of person Martius is, particularly when he refuses to court them in order to be made consul. You might look at Martius's pride and snobbery in terms of the way he treats other people.