Coues was born in Portsmouth, New Hampshire, to Samuel Elliott Coues and Charlotte Haven Ladd Coues. He graduated at Columbian University, Washington, D.C., in 1861, and at the Medical school of that institution in 1863. He served as a medical cadet in Washington in 1862–1863, and in 1864 was appointed assistant-surgeon in the regular army, and assigned to Fort Whipple, Arizona. While there was not yet any legal provision for divorce under its laws, the 1st Arizona State Legislature granted Coues an annulment of his marriage to Sarah A. Richardson.