Range and charge anxiety remain essential barriers to a faster electric vehicle market diffusion. To this end, quickly and reliably finding suitable charging stations may foster an electric vehicle uptake by mitigating drivers' anxieties. Here, existing commercial services help drivers to find available stations based on real-time availability data but struggle with data inaccuracy, e.g., due to conventional vehicles blocking the access to public charging stations. In this context, recent works have studied stochastic search methods to account for availability uncertainty in order to minimize a driver's detour until reaching an available charging station. So far, both practical and theoretical approaches ignore driver coordination enabled by charging requests centralization or sharing of data, e.g., sharing observations of charging stations' availability or visit intentions between drivers.Against this background, we study coordinated stochastic search algorithms, which help to reduce station visit conflicts and improve the drivers' charging experience. We model a multi-agent stochastic charging station search problem as a finite-horizon Markov decision process and introduce an online solution framework applicable to static and dynamic policies. In contrast to static policies, dynamic policies account for information updates during policy planning and execution. We present a hierarchical implementation of a single-agent heuristic for decentralized decision making and a rollout algorithm for centralized decision making. Extensive numerical studies show that compared to an uncoordinated setting, a decentralized setting with visit-intentions sharing decreases the system cost by 26%, which is nearly as good as the 28% cost decrease achieved in a centralized setting, and saves up to 23% of a driver's search time while increasing her search reliability.