Gunter was born in Alexandria, the seat of Rapides Parish and the largest city in Central Louisiana, to Carl N. "Euddie" Gunter, Sr. (June 23, 1916 – November 10, 1975), and Gladys Slay Gunter Richardson (April 18, 1920 – January 14, 2009) His paternal grandparents were John Gunter (January 31, 1886 – July 26, 1963) and Mary Hooper Gunter (May 21, 1895 – January 6, 1976). His maternal grandparents were Charles O. "Buck" Slay, Sr. (November 3, 1894 – September 10, 1967), and the former Louella Sullivan (September 22, 1899 – December 13, 1996). Gunter was a maternal nephew of former Rapides Parish Assessor Charles O. Slay Jr.