Especially in developing regions, parents are rarely given a direct voice in the design of digital maternal and child health (MCH) interventions. Instead, MCH needs and requirements are driven by organizations and health workers. In this research, we engage with both rural and urban parents and community leaders to better understand their challenges and priorities for digital MCH and propose a parent-centered agenda for human-computer interaction research. This paper reports on the community-based, digital MCH priorities identified in our research, and describes how we approached community discourse and co-design of digital initiatives for these priorities, through parent-centered workshops with low-resource South African communities. Furthermore, we provide the parent-centered design opportunities and tensions we discovered for digital MCH in South African contexts, such as designing for local contexts and languages, designing for accessibility and connectedness, and highlighting the underdeveloped digital MCH niches. Finally, we highlight the importance of including facilitators for co-design workshops, such as using intermediaries and design cards.