Safety and robustness need to be key features of future cislunar spacecraft. As human presence near the moon expands and spacecraft begin to operate more autonomously, efficient and verifiable guidance, navigation, and control algorithms must be employed. A necessary mission component for spacecraft that operate in the L2 region about the Moon is stationkeeping, whereby a spacecraft uses its propulsion system to maintain some reference orbit. The generation of stationkeeping maneuvers can be a limiting factor for cislunar missions, and thus the move towards autonomous spacecraft operation in the L2 regime could accelerate and augment mission capabilities. This thesis presents the application of stochastic optimal control for an L2 near-rectilinear quasi-periodic halo orbit stationkeeping strategy. The stationkeeping problem is formulated as a trajectory optimization problem with non-stationary boundary conditions and covariance control which is solved using sequential convex programming. With this technique, stationkeeping maneuvers can be efficiently computed with assurances of robustness to disturbances resulting from the dynamical environment, input actuation error, and state estimation error.