After ending his active football career, Schjønberg changed into the coaching business when he became youth coach at 1. FC Kaiserslautern in July 2003. He moved to Denmark in July 2004, to coach Danish Superliga club Herfølge BK, alongside his good friend Allan Nielsen. Herfølge BK were relegated to the Danish 1st Division, but Schjønberg kept his job. In November 2005, he became assistant coach of Hannover 96 to manager Peter Neururer. When Neururer was fired in September 2006, Schjønberg deputised as head coach for a single DFB-Pokal match, where Hannover 96 eliminated Dynamo Dresden. When Hannover 96 hired Dieter Hecking as new head coach, he brought Dirk Bremser with him as assistant coach, and Schjønberg became the coach of the amateur ranks of the club.