Decentralized online planning can be an attractive paradigm for cooperative multi-agent systems, due to improved scalability and robustness. A key difficulty of such approach lies in making accurate predictions about the decisions of other agents. In this paper, we present a trainable online decentralized planning algorithm based on decentralized Monte Carlo Tree Search, combined with models of teammates learned from previous episodic runs. By only allowing one agent to adapt its models at a time, under the assumption of ideal policy approximation, successive iterations of our method are guaranteed to improve joint policies, and eventually lead to convergence to a Nash equilibrium. We test the efficiency of the algorithm by performing experiments in several scenarios of the spatial task allocation environment introduced in [Claes et al., 2015]. We show that deep learning and convolutional neural networks can be employed to produce accurate policy approximators which exploit the spatial features of the problem, and that the proposed algorithm improves over the baseline planning performance for particularly challenging domain configurations.