Thitherto he had been the advocate of St Andreas at Freising since 1150 and Count of Dachau (as Conrad II) from 1152.
Conrad married Adelaide, daughter of Henry, Duke of Lower Lorraine, sometime before 1140.
His second wife, Matilda of Falkenstein, gave him one son, Conrad II, who inherited Merania and, in 1172, Dachau.
In late June or early July 1152, the Frederick I granted Conrad the title of duke for his lands around the Kvarner Gulf, possibly as a reward for helping Frederick secure the throne after the king's death.
He used the title dux Meranus to refer to his coastal territory, but Bishop Otto I of Freising, in his history of Frederick's reign, calls him "Duke of Dalmatia and Croatia".