[1] His paternal grandfather was the abolitionist minister Samuel Hanson Cox and his uncle was Arthur Cleveland Coxe, the Episcopal Bishop of Western New York.

His maternal grandfather was Alfred Conkling, who served as a U.S. Representative from upstate New York and a judge in the Northern District.

[3] On April 24, 1882 Coxe was nominated by President Chester A. Arthur to a seat on the United States District Court for the Northern District of New York vacated by Judge William J. Wallace.

He was confirmed by the United States Senate on May 4, 1882, and received his commission the same day.

[5] Together, they were the parents of five children: Coxe died on April 15, 1923, in Hartford, Connecticut.

[5] Through his son Charles, he was a grandfather of Louis Osborne Coxe (1918–1993), the poet and playwright best known for writing the Broadway version of Billy Budd.