Coppola started his career at the age of eight with the Metropolitan Opera Children’s Chorus. At the age of 9 he was in the Met's debut of Turandot. He served as an army bandmaster during World War II, conductor at Radio City Music Hall and director of both the Symphony and Opera Departments at the Manhattan School of Music. He earned a bachelor's degree (1964) and a master's degree (1965) in composition from Manhattan School of Music and received honorary Doctorates from the University of Tampa and Quinnipiac University in Connecticut.
Coppola's first marriage was to Marion Jane Miller, a ballet dancer, with whom he had one child, Susan Marion Coppola (1943–2008). After their divorce, he wed Almarinda Drago, also a ballet dancer, with whom he had two children, Lucia and Bruno Coppola.
He turned 100 in March 2017.
Among his works are a violin concerto, a symphony, and Sacco and Vanzetti, an opera in both Italian and English about immigrants Sacco and Vanzetti. In the 1950s and 1960s, Coppola was the musical director of six Broadway musicals, including Silk Stockings, Bravo Giovanni and The Boy Friend. He conducted two film scores, 1990's The Godfather Part III and 1992's Dracula. He appeared in the former, shown conducting Cavalleria rusticana in the Teatro Massimo of Palermo.
He debuted with the New York City Opera in 1965, conducting the world premiere of Jack Beeson's Lizzie Borden, and led performances of Carmen (with Beverly Wolff, Richard Cassilly and Norman Treigle), La traviata, Il barbiere di Siviglia, and Madama Butterfly during the same year. At the Seattle Opera in 1970, Coppola led the world premiere of Carlisle Floyd's Of Mice and Men.
Coppola helped to found Opera Tampa in 1996 and served as its Founding Artistic Director. Among his numerous productions with the company was the world premier of Sacco and Vanzetti on March 17, 2001. He retired from the position in 2012.
Coppola was honored with the Lifetime Achievement Award from the Puccini Foundation and recognized by the Italian government as Cavaliere, Gran Ufficiale.
Coppola collaborated with the Orchestra Sinfonica di Milano Giuseppe Verdi, also known as Orchestra Verdi, and operatic soprano Angela Gheorghiu on a recording of Puccini works for EMI. This recording was later re-released with additional tracks recorded by Pappano and the Royal Opera House Orchestra, Covent Garden.
In 2008, Opera Tampa announced that an award was to be established in his name. The Anton Coppola Excellence in the Arts Award is presented annually to recognize an artist for significant contributions to Opera Tampa and the music world at large, and specifically for extraordinary work in the cultivation and care of the operatic art form. Coppola himself was recipient of the award in 2012, the year of his retirement.The Godfather Part III (1990) - Conductor of 'Cavalleria Rusticana' (uncredited)