Born in Rhinebeck, New York, he was the son of Dr. Ananias Cooper and Elizabeth DeKay Cooper.
He studied medicine with Dr. Crosby in New York City and became a physician, like his father. By 1791, Cooper had settled in Albany. In 1792, he began to practice medicine.
Career
In 1794, he was appointed Health Officer of the Port of Albany
In February 1804, Cooper attended a dinner party during which Alexander Hamilton spoke forcefully and eloquently against the Federalists' plan to nominate Aaron Burr as their candidate for Governor of New York. Cooper later wrote a letter to Philip Schuyler, Alexander Hamilton's father-in-law, in which he made reference to the "despicable opinion" Hamilton had expressed about Burr. The letter was published in The Albany Register, but was tame compared to other attacks on Burr in the press. Still, Cooper's letter proved the last straw in the ongoing rivalry between Burr and Hamilton. When Burr read the letter weeks later, shortly after his defeat in the governor's race, he was enraged by Hamilton's alleged remarks, and challenged Hamilton to a duel, in which Hamilton was killed.
He married Margaret Vernor (c. 1774–1860), the adopted daughter of the future Lt. Gov.John Tayler and the former Margarita Van Valkenburgh. They had five children, including:
John Tayler Cooper (1798–1878), a lawyer and Major-General who married a daughter of John Vernon Henry.
Charles DeKay Cooper (1813–1902), a Reverend who married Cornelia Lansing Sutherland, a granddaughter of Chancellor John Lansing Jr.
Death and burial
Cooper died on January 30, 1831. He was buried in the Dutch Reformed section of the State Street Burying Grounds, but his remains were later removed to a family plot in the Albany Rural Cemetery.
Report submitted by the Canal Commission on March 8, 1816, to the State Assembly, signed by Cooper, in Niles Weekly Register (Vol. 10, March 1816, page 101)
Death date from The Annals of Albany Vol. VI, by Joel Munsell (re-published by BiblioBazaar, LLC, 2008, ISBN0-559-28203-6, ISBN978-0-559-28203-4, page 142) {The burial ground inscription says "...in the 60th year of his age." but all sources give 1769 as birth year, which means he died in his 62nd year.]