Coyer had run the team's defense since 2009 when he was one of the first hirings by then new head coach Jim Caldwell.
The Colts, who have yet to win a game this season, have the 29th-ranked defense in the league, allowing 389.4 yards and 29.7 points a game.
"We feel this is the most effective and realistic way to move forward and win games this season," Caldwell said in a statement. "We appreciate all of the effort and hard work Larry Coyer put forth in his three years with the Colts."
Murphy has spent the past 14 years with Indianapolis as the linebackers coach and has not been a defensive coordinator since holding the job from 1979-83 with the Saskatchewan Roughriders of the Canadian Football League.