This paper addresses the problem of resource allocation in formations of mobile robots localizing as a group. Each robot receives measurements from various sensors that provide relative (robot-To-robot) and absolute positioning information. Constraints on the sensors' bandwidth, as well as communication and processing requirements, limit the number of measurements that are available or can be processed at each time step. The localization uncertainty of the group, determined by the covariance matrix of the equivalent continuous-Time system at steady state, is expressed as a function of the sensor measurements' frequencies. The trace of the submatrix corresponding to the position estimates is selected as the optimization criterion, under linear constraints on the measuring frequency of each sensor and the cumulative rate of EKF updates. This formulation leads to a convex optimization problem whose solution provides the sensing frequencies, for each sensor on every robot, required in order to maximize the positioning accuracy for the group. Simulation experiments are presented that demonstrate the applicability of this method and provide insight into the properties of the resource-constrained cooperative localization problem.