In 1940 Sour worked for Broadcast Music as its lyrics editor, and by 1966 had risen through company ranks to become BMI's president. Two years later he had become the company's vice chairman and was instrumental in establishing BMI's musical theater workshop. He retired in 1970.
Working with lyricists Edward Heyman and Frank Eyton and composer Johnny Green, Sour wrote the lyrics to the ballad "Body and Soul". In partnership with Una Mae Carlisle (1915–1956), he also composed lyrics for the song "Walkin' by the River", which became a radio hit as sung by Syliva Froos (1927–2004) in 1941. Ella Fitzgerald recorded "Walkin' by the River" for Decca Records, with Leroy Kirkland directing the orchestra. Benny Carter also recorded "Walkin", with Carlisle on vocals. Sour composed music and lyrics for both film and theater; along with Henry Katzman, he wrote the soundtrack sections "Twitterpated" and "Thumper's Song" for the Walt Disney Productions animated feature Bambi.