His songwriting career began in the early 1950s with material he contributed to revues staged in New York City by Ben Bagley and Julius Monk.
In 1964, he composed The Brightest Show on Earth for the World's Fair held in what is now Flushing Meadows-Corona Park.
Richardson's first and most notable Broadway theatre score was for the 1971 adaptation of Truman Capote's The Grass Harp.
Other Broadway credits include incidental music for the 1978 revival of The Royal Family with Rosemary Harris and Eva Le Gallienne, the 1980 revival of The Philadelphia Story with Blythe Danner, and the original play The Curse of an Aching Heart with Faye Dunaway in 1982.
Richardson also composed jingles for television and radio commercials as well as scores for industrial shows and sponsored films.