De Koning played for AZ'67 for ten years (1978–1988) before moving to FC Twente, where he became known as "Hansje de King" (Hans the King) and played 140 games in five seasons with the club before being forced to retire in 1993 after suffering a serious injury aduring Fred Rutten's farewell match, .
After his retirement as a player, de Koning then became a goalkeeping coach for his former club AZ, also serving briefly as joint caretaker in 1997, and later on moved into head management at Eerste Divisie (Dutch second division) level debutting at such role with Limburgish club Fortuna Sittard, and then briefly serving as interim coach of FC Dordrecht from March to July 2005 before being appointed at TOP Oss (later renamed FC Oss) later that year; he filled such role until June 2010, when he was removed after he failed to save FC Oss from relegation to the newly established Topklasse level at the end of the 2009–10 Eerste Divisie.
From July 2010 he is in charge of Eerste Divisie club AGOVV Apeldoorn. In March 2011 it was announced AGOVV and de Koning would part ways at the end of the season; de Koning was then unveiled later in May as new head coach of Helmond Sport for the 2011–12 season. On 21 April 2012, it was confirmed that he would be in charge of Eerste Divisie club Volendam for the 2012-13 season. He signed a two-year contract.