Coy played Future U.S. President Thomas Jefferson in the 1955 episode "Eli Whitney Invents the Cotton Gin (May 27, 1793)" on the CBS anthology You Are There, a look at the Inventor Eli Whitney and the cotton gin, which greatly enhanced the cultivation of cotton. He portrayed U.S. Senator and 1860 Democratic presidential nominee Stephen A. Douglas of Illinois in the 1957 episode "Springfield Incident" of CBS's The 20th Century Fox Hour. He also played a prosecutor on the same series in 1956 in the episode "The Last Patriarch." Coy made four guest appearances on Perry Mason, including the role of murder victim Denver Leonard in the 1960 episode, "The Case of the Prudent Prosecutor."

Coy performed on Broadway from 1930–1948. He appeared in several early Group Theatre productions. He was the first actor to play Lone Wolf on the radio series of the same name.

Coy's other film appearances included The Lusty Men (1952), Gunmen from Laredo, The Gunfight at Dodge City, and North by North West (all 1959), and as Ike Garvey in Five Guns to Tombstone (1960).

Coy also appeared on Jim Davis' western anthology series, Stories of the Century in the role of Sam Clayton in the 1954 episode entitled "Tom Horn," an account of the western lawman-turned outlaw Tom Horn. He appeared on many other western television programs, including Cheyenne, Bronco, Cimarron City, The Lone Ranger, The Life and Legend of Wyatt Earp (one episode as Ben Thompson), Shotgun Slade, The Deputy, Bonanza, Bat Masterson, The Adventures of Jim Bowie, Trackdown, Tales of Wells Fargo, Yancy Derringer, Laramie, Two Faces West, Lawman, Wanted: Dead or Alive, The Restless Gun, The Rough Riders, Dick Powell's Zane Grey Theatre, Pony Express, Rawhide, Mackenzie's Raiders, Have Gun – Will Travel, The Texan, The Man from Blackhawk, Hotel de Paree, Overland Trail, Maverick, The Virginian, The Big Valley, Laredo, The Outcasts, Wagon Train (five times), and Robert Conrad's The Wild Wild West.

Coy appeared as John Wayne's doomed brother in the early sequences of the 1956 film The Searchers. In 1957, Coy portrayed. Dr. Joseph Warren in the Walt Disney film Johnny Tremain, based on the 1943 Esther Forbes historical novel of the American Revolution. Warren was the physician who operates successfully on the accidentally burned hand of title character Johnny Tremain, an apprentice silversmith, played by Hal Stalmaster, who one day had expected to own his own shop and become wealthy. Dr. Warren, a spy for the Patriots, was thereafter killed six days after his 34th birthday fighting as a Common soldier in the Battle of Bunker Hill in Boston, Massachusetts.

He appeared in the anthology series, Schlitz Playhouse of Stars and Four Star Playhouse (four times each) and The Loretta Young Show (three times). He played a Confederate States of America general in the 1959 episode entitled "Corporal Hardy" of another anthology series, Alcoa Theatre. He played Dr. Steele in the 1960 episode "The House in Order" on NBC's The Barbara Stanwyck Show. Coy also appeared in all three of Rod Cameron's 1950s syndicated series, City Detective, State Trooper, and COronado 9.

Coy's last television role was as Chief Blackfish in the 1970 episode "How to Become a Goddess" on the NBC series Daniel Boone, starring Fess Parker as Kentucky frontiersman Daniel Boone. Coy died of congestive heart failure at the age of 65 in Santa Maria, California.