There's not going to be a state association that covers all youth football in the state. Pop Warner website shows three leagues in the state; each of these would cover several towns. That's at:
http://www.popwarner.com/admin/tennessee.asp
If it's a town-organized league, find the head of the parks dept. Or, hell, just talk to the mayor or town council. Somebody will be able to point you in the right direction.