Parents use mobile monitoring software to observe and restrict their children's activities in order to minimize the risks associated with Internet-enabled mobile devices. As children are stakeholders in such technologies, recent research has called for their inclusion in its design process. To investigate children's perceptions of parental mobile monitoring technologies and explore their interaction preferences, we held two co-design sessions with 12 children ages 7-12. Children first reviewed and redesigned an existing mobile monitoring application. Next, they designed ways children could use monitoring software when they encounter mobile risks (e.g., cyberbullying, inappropriate content). Results showed that children acknowledged safety needs and accepted certain parental controls. They preferred and designed controls that emphasized restriction over monitoring, taught risk coping, promoted parent-child communication, and automated interactions. Our results benefit designers looking to develop parental mobile monitoring technologies in ways that children will both accept and can actively benefit from.