Reservoir computing is a biologically inspired class of learning algorithms in which the intrinsic dynamics of a recurrent neural network are mined to produce target time series. Most existing reservoir computing algorithms rely on fully supervised learning rules, which require access to an exact copy of the target response, greatly reducing the utility of the system. Reinforcement learning rules have been developed for reservoir computing, but we find that they fail to converge on complex motor tasks. Current theories of biological motor learning pose that early learning is controlled by dopamine-modulated plasticity in the basal ganglia that trains parallel cortical pathways through unsupervised plasticity as a motor task becomes well learned. We developed a novel learning algorithm for reservoir computing that models the interaction between reinforcement and unsupervised learning observed in experiments. This novel learning algorithm converges on simulated motor tasks on which previous reservoir computing algorithms fail and reproduces experimental findings that relate Parkinson's disease and its treatments to motor learning. Hence, incorporating biological theories of motor learning improves the effectiveness and biological relevance of reservoir computing models.