Pro-Air operates pt 135 out of BNA. I think they fly Cessna 310s.
Executive Air Express is based at MQY, just east of Nashville, they operate part 135 and part 91 flights in Merlins, C-303's, C-421s, and a King Air.
As mentioned previously,
Flight Express is in Nashville, they mostly fly checks and operate part 135 in C-210's and Barons.
You can also look into
Colemill, they do charter ops in King Airs and a Navajo from Cornelia Fort.
You can also try to get on with
Corporate Flight Management or Regions, both of which are at MQY.
Hope this helps.