Today, Conversational Agents (CA) are deeply integrated into the daily lives of millions of families, which has led children to extensively interact with such devices. Studies have suggested that the social nature of CA makes them a good learning companion for children. Therefore, to understand children's preferences for the use of CAs for the purpose of in-home learning, we conducted three participatory design sessions. In order to identify parents' requirements in this regard, we also included them in the third session. We found that children expect such devices to possess a personality and an advanced level of intelligence, and support multiple content domains and learning modes and human-like conversations. Parents desire such devices to include them in their children's learning activities, foster social engagement, and to allow them to monitor their children's use. This understanding will inform the design of future CAs for the purpose of in-home learning.