We have previously proposed a novel hardware platform (SOEN) for neuromorphic computing based on superconducting optoelectronics that presents many of the features necessary for information processing in the brain. Here we discuss the design and training of networks of neurons and synapses based on this technology. We present circuit models for the simplest neurons and synapses that we can use to build networks. We discuss the further abstracted integrate and fire model that we use for evolutionary optimization of small networks of these neurons. We show that we can use the TENNLab evolutionary optimization programming framework to design small networks for logic, control and classification tasks. We plan to use the results as feedback to inform our neuron design.