From the TSSAA site:
Schools that have won more than one state championship in Football
School Titles Years
Alcoa (5) 1977,1978,1979,1989,2000
Austin East (3) 1983,1986,2001
Battle Ground Academy (5) 1995,1997,1998,2001,2003
Bishop Byrne (2) 2001,2002
Brentwood Academy (9) 1974,1980,1981,1982,1987,1988,1991,1995,1996
Christ Presbyterian Academy (2) 2000,2002
Cleveland (3) 1993,1994,1995
David Lipscomb (2) 1994,2002
Donelson Christian Academy (2) 1988,1996
Evangelical Christian School (3) 1983,1999,2000
Father Ryan (2) 1974,1997
Gallatin (3) 1978,1989,1992
Germantown (2) 1983,2003
Goodpasture (3) 1995,1999,2001
Lake County (2) 1980,1985
Lincoln County (3) 1982,1990,1993
Loudon (3) 1969,1974,1975
Marion County (4) 1990,1992,1994,1995
Maryville (7) 1970,1976,1978,1998,2000,2001,2002
Melrose (2) 1996,1998
Milan (4) 1971,1977,1998,1999
Montgomery Bell Academy (5) 1998,1999,2000,2002,2003
Oak Ridge (4) 1975,1979,1980,1991
Oakland (2) 1984,1998
Pearl Cohn (2) 1996,1997
Riverdale (3) 1994,1997,2001
South Pittsburg (3) 1969,1994,1999
Sweetwater (3) 1971,1972,1993
Tennessee (2) 1971,1972
Trousdale County (5) 1972,1990,1993,1997,1998
Webb School of Knoxville (2) 1981,1996