Consider a set of agents in a peer-to-peer communication network, where each agent has a personal dataset and a personal learning objective. The main question addressed in this paper is: how can agents collaborate to improve upon their locally learned model without leaking sensitive information about their data? Our first contribution is to reformulate this problem so that it can be solved by a block coordinate descent algorithm. We obtain an efficient and fully decentralized protocol working in an asynchronous fashion. Our second contribution is to make our algorithm differentially private to protect against the disclosure of any information about personal datasets. We prove convergence rates and exhibit the trade-off between utility and privacy. Our experiments show that our approach dramatically outperforms previous work in the non-private case, and that under privacy constraints we significantly improve over purely local models.