Scientific support invited by Indigenous peoples and local communities (IPLC) to assist with customary environmental management can improve conservation and community livelihoods. For example, demographic models can help to understand how alternative wildlife management strategies affect population dynamics and harvest sustainability. We developed a demographic model to assist Ngāi Tahu, the southern-most Māori tribe in Aotearoa/New Zealand, in customary management of a culturally important population of Black Swans (kakī anau, Cygnus atratus). We used recent demographic data, including results of an experimental egg harvest study, to inform tangata tiaki (Ngāi Tahu environmental guardians) about how customary egg harvest and background pressure from sport hunting of swans aged ≥ 1 year differentially affect population growth. We also assessed how sport hunting of swans affects the sustainability of customary egg harvest. Estimated population growth (1.018 or presently growing 1.8% annually; 95% CI: 0.808-1.241) was most sensitive to changes in adult and subadult survival, followed by juvenile (first-year) survival, breeding propensity, and nest hatching success. Uncertainty in population growth was almost entirely attributable to uncertainty in swan survival rates after hatching. Sustainable population-level rates of egg harvest varied from none to more than half of all eggs, depending on small changes in adult and subadult survival. Population sensitivity to adult and subadult survival suggests that limiting and monitoring their mortality are crucial to population and egg harvest sustainability, whereas contemporary government-mandated species management, through Fish and Game New Zealand, allows adult and subadult mortality from sport hunting, with little record of offtake. Recognizing the rights and interests of Ngāi Tahu, and monitoring swan mortality more closely, could improve Ngāi Tahu abilities to practice customary harvest, enhance population and environmental monitoring, and, when appropriate, control swan numbers in a culturally appropriate and less wasteful way. The model we present could aid decision making and communication between Ngāi Tahu and New Zealand's Crown government within a potential future co-management arrangement. Demographic models can be useful tools for supporting customary environmental management, but developing, maintaining, and implementing these tools requires support for adaptive policies and management arrangements that recognize IPLC rights to the environment and decision making.