In their fashion they did at least half of what you ask. In his book "Look Away: A History of the Confederate States of America" William C. Davis talks about whole sections of states like Alambama and Mississippi where whole counties were held by deserters and draft-dodgers and where representatives of the confederate government dared not go. Governors did their best to undermine conscription by allowing increases in militia and state employees. Were their riots like up North? No. It was worse. It was a concerted effort by civil authority to undermine conscription imposed by the central government. How can you compare civil unrest to that?
They could have pulled a Lincoln and invaded them, killing thousands?