Coopersmith was born August 11, 1925, in New York City, working an early job as an office boy for what was then known as The Shubert Theatrical Company at the age of 16. During World War II, he served with the 94th Infantry Division of the United States Army, earning a Purple Heart. After the war, Coopersmith earned a degree from New York University.
He began his writing career in TV, writing for the quiz show Americana in 1947. He would spend the rest of the '40s and '50s writing for a number of television programs of varying acclaim, including The Gabby Hayes Show, Johnny Jupiter, Armstrong Circle Theater, and others.
He would make his Broadway debut as the book writer for the 1965 musical Baker Street, an attempt to musicalize the detective stories of Sherlock Holmes, working with songwriters Marian Grudeff and Raymond Jessel. The work was a modest success running for the better part of a year and 311 performances, and Coopersmith was rewarded with a 1965 Tony nod for Best Author of a Musical for his book. The following year, Coopersmith was credited with "Additional Book Material" for The Apple Tree, a comedic Jerry Bock-Sheldon Harnick musical that has been better remembered in the years since its 1965 debut. Coopersmith reportedly wrote the script for the first of the musical's three one-act tales, with Coopersmith's portion based on Mark Twain's The Diary of Adam and Eve and Eve's Diary.
Coopersmith would find his greatest success with TV's Hawaii Five-O. After writing the series' fourth episode, Coppersmith spent eight years on the police procedural, writing 30 hour-long episodes and two feature-length movies. Among his other screen credits: the Rankin/Bass 'Twas the Night Before Christmas, starring Broadway favorites Joel Grey and Tammy Grimes.
Though Coopersmith would never get a stage work back to the Main Stem after The Apple Tree, he continued to work on stage projects. He collaborated with Martin Charnin and Edward Thomas on Mata Hari, about the infamous alleged spy. The work would play a brief run Off-Broadway at what is now the Lucille Lortel Theatre under the title Ballad for a Firing Squad. Coopersmith joined Mary Rodgers and Sheldon Harnick to write an adaptation of Pinocchio for Bil Baird's Marionette Theater, which ran Off-Broadway in 1974. Next up was an adaptation of Swiss Family Robinson for Barry and Fran Weissler's National Theater Company, which toured plays and musicals to schools around the country. He also adapted Ruth Gruber's Haven, recounting her experience rescuing 1,000 Holocaust refugees, with William Goldstein and Joe Darion in the early '90s, a work that would ultimately get a production at Los Angeles' Gindi Theater in 2001.
Coopersmith also wrote a number of plays for the stage, including an Eleanor Roosevelt bioplay titled Eleanor; The Mystery of Anna O, about the first person to be psychoanalyzed; Reflections of a Murder, about the mysterious death of a ballerina; and The Other Side, about a real-world clash between Harry Houdini and Sir Arthur Conan Doyle.
Coopersmith is survived by two daughters, Amy Coopersmith Lauria and Jill Andrea Lambert; six grandchildren and step-grandchildren; and four great-grandchildren. Memorial donations are requested for Rochester Regional Health, Unity Hospital.