Coy is a lifelong Iowan who earned his elementary education degree with a middle school endorsement from the University of Iowa. He worked as a substitute teacher and special education paraeducator in the Iowa City Community School District after graduation and his first teaching position was as a 6th grade social studies and English teacher in the East Marshall Community School District. He returned to Iowa City to teach 7th and 8th grade language arts and coach. In Iowa City, he served as head bargainer and local president for the Iowa City Education Association and served on the ISEA PAC Central Committee.
Coy moved to staff work for the ISEA in 2006 and served as UniServ director in the Iowa City and Cedar Rapids area until 2016 when he was promoted to associate director of affiliate services overseeing the UniServ program.
Coy is married to Kirsten Running-Marquardt, former Iowa state representative and now Linn County supervisor. They have one son, Jack.