There's not a lot of early pro teams in the south (you're in NFL south), so IMO staying geographically true would become a hard task.
Sticking to defunct NFL teams, there's only three that I can find... Dallas Texans, LA Buccaneers, and Louisville Brecks/Colonels.
Of course, teams don't have to be from the NFL. Any pro level American football league fits the theme. Pre-NFL, AFL, USFL, former (non-active) XFL teams, etc... (These are how I see it, as a former admin for this league. Gustoon may wish to amend these if he has a different view.