While rich medical datasets are hosted in hospitals distributed across the world, concerns on patients' privacy is a barrier against using such data to train deep neural networks (DNNs) for medical diagnostics. We propose Dopamine, a system to train DNNs on distributed datasets, which employs federated learning (FL) with differentially-private stochastic gradient descent (DPSGD), and, in combination with secure aggregation, can establish a better trade-off between differential privacy (DP) guarantee and DNN's accuracy than other approaches. Results on a diabetic retinopathy~(DR) task show that Dopamine provides a DP guarantee close to the centralized training counterpart, while achieving a better classification accuracy than FL with parallel DP where DPSGD is applied without coordination. Code is available at https://github.com/ipc-lab/private-ml-for-health.