With the increasing number of cislunar space missions, real-time and reliable navigation and communication services have become critical. It is necessary to develop the navigation constellations dedicated to cislunar space services. However, there are plenty of orbits in cislunar space providing alternative orbits, which makes constellation design a challenging task. To address this, this paper proposes a method for a cislunar navigation constellations configuration design via orbits with resonant periods. First, a periodic orbit catalog for the Earth–Moon system is constructed. Baseline orbits are selected from different orbital families, and all resonant orbits with periods proportional to the baseline orbits are compiled into a resonant orbit set. Second, a Dilution of Precision (DOP) model for navigation performance and a spatial zoning model are established. Then, resonant orbital combinations are screened based on orbital type composition, followed by resonance constellation generation according to predetermined constellation scales. All constellation configurations are categorized by orbital type to obtain a full resonant constellation set. Finally, the proposed method is applied to design optimal configurations providing navigation services for near-Earth and lunar regions. The simulation results shows that constellations combining L2 southern/northern Near-Rectilinear Halo Orbits (NRHOs) with vertical orbits at L4/L5 points deliver the optimal navigation performance in cislunar regions. The relationships between orbital radius and DOP values in target areas, as well as the DOP evolution patterns over constellation periods, are analyzed. The mean DOP values of the optimal constellation in both the near-Earth region and the lunar region increase as the spatial radius expands.