We consider the problem of cooperative localization (CL) via interrobot measurements for a team of networked robots with limited on-board resources. We propose a novel algorithm in which each robot localizes itself in a global coordinate frame by local dead reckoning, and opportunistically corrects its pose estimate whenever it receives a relative measurement update message from a server. The computation and storage cost per robot in terms of the size of the team is of order $O(1)$, and the robots are only transmitting information when they are involved in a relative measurement. The server also only needs to compute and transmit update messages when it receives an interrobot measurement. Under perfect communication, our algorithm is an alternative implementation of a joint CL for the team via an extended Kalman filter. However, perfect communication is not a hard constraint. We show that our algorithm is robust to communication failures, with formal guarantees that the updated estimates of the robots receiving the update message are of minimum variance in a first-order approximate sense at that given timestep. We demonstrate the performance of our algorithm in simulation and experiments.