FoxRentaCar.com has lower than normal minimum age requirements... but, they do not currently have any locations in Nashville.
The only other possible exceptions to this rule would be for active duty military personnel or federal government employees. You can also check to see if the company that you work for has a corporate account with any car rental companies. Many larger businesses and companies will contract rates with their preferred car rental company(s) and will negotiate a lower minimum age to rent for their employees.
If you own your own business, you can also check into setting up a business account with one or more auto rental companies and seeing if you can get a program that will allow you to get a rental car under 21 years of age.
You may also have some luck by searching outside the larger, big brand national rental car companies regarding rental car under 21 policies.
I did a bit of checking and found this information about Rent-A-Wreck:
"Usually, Rent-A-Wreck requires renters to be at least 18 years old, but some locations may require a minimum age of 25 years. For consumers under 25, a credit card is usually required for payment and the rental rate may be higher. Please contact the individual Rent-A-Wreck car rental location for their specific age policies. "
Their location info is:
Rent-A-Wreck of Nashville
201 Donelson Pike
Nashville, TN 37214
(800) 944-7501
Although they had no websites, you may also want to check:
Discount Rent A Car
Serving the Nashville Area
(615) 366-6622
and
Tennessee Car And Van Rental
2408 Lebanon Pike Cir
Nashville, TN 37210