Hi Suzanne
The Mississippi Department of Archives & History, Jackson, MS, hold radio recording from the Civil Rights era. Also, you may find some at Jackson State University, Jackson MS, & the University of Southern Mississippi, Hattiesburg, MS. I believe the ones at MDAH are from WLBT and cover some of the riots at Jackson State and Alcorn College.
Special Collections Strozier Library Florida State University Tallahassee, FL 32306-2047