Konrad was the son of unknown parents. The date and place of his birth have not been found.
His wife was Anna Constantia von Fürstenberg-Heiligenberg, who he married in 1604. The place has not been found. They had no known children.
| Attribute | Date | Description | Details | Source | Multimedia | Notes |
|---|---|---|---|---|---|---|
| Nobility Title | freiherr von Bemelberg |