For tasks where the dynamics of multiple agents are physically coupled, e.g., in cooperative manipulation, the coordination between the individual agents becomes crucial, which requires exact knowledge of the interaction dynamics. This problem is typically addressed using centralized estimators, which can negatively impact the flexibility and robustness of the overall system. To overcome this shortcoming, we propose a novel distributed learning framework for the exemplary task of cooperative manipulation using Bayesian principles. Using only local state information each agent obtains an estimate of the object dynamics and grasp kinematics. These local estimates are combined using dynamic average consensus. Due to the strong probabilistic foundation of the method, each estimate of the object dynamics and grasp kinematics is accompanied by a measure of uncertainty, which allows to guarantee a bounded prediction error with high probability. Moreover, the Bayesian principles directly allow iterative learning with constant complexity, such that the proposed learning method can be used online in real-time applications. The effectiveness of the approach is demonstrated in a simulated cooperative manipulation task.