Prior to working as a head coach, Donnan served as an assistant coach at several schools, including Kansas State University, University of Missouri, Florida State University, and the University of Oklahoma. Donnan was the offensive coordinator at Oklahoma from 1985 to 1989. From 1985 to 1988, he coached under Barry Switzer, a member of the College Football Hall of Fame and a Super Bowl winning coach. Donnan coached the legendary Oklahoma Sooner wishbone offense that helped the Sooners to three consecutive 11–1 seasons from 1985–1987, and a national championship in 1985. In 1986, the Sooners scored 508 points, which at the time was the second highest point total in the school's storied history, trailing only the Sooners 1971 NCAA record setting rushing offense that scored 534 points.