Cotter was the second son of a stay-at-home mother and a father who worked at a Chevrolet plant as a director of industrial relations, neither of whom had attended college.
After finishing the fellowship in 1966, he became the representative of the Ford Foundation in Colombia and Venezuela, in which capacity he participated in programs to support economic planning, modern agriculture, the teaching of science, adult education on television, family planning, and the reform of legal education (including an exchange program with Harvard Law School).
He returned to New York in 1970 to coordinate the foundation's educational programs before becoming the president of the African-American Institute (AAI) where he served for nine years.
Cotter and his wife, Linda, lived in Concord, Massachusetts, and spent the winter months in Longboat Key, Florida.
He was (as of 2014) a consultant to the Robertson Foundation on their African Programs, treasurer of the Massachusetts Historical Society, and instructor on the Supreme Court at Pierian Springs Academy in Sarasota Florida.