Non-orthogonal multiple access (NOMA) can multiplex different users on a single channel by applying superposition coding at the transmitter and Successive Interference Cancellation (SIC) at the receiver. It is considered to be an important technology for next generation wireless communications to achieve high throughput and large-scale connectivity. To take advantage of the effectiveness of NOMA, in addition to pairing users using criteria based on distance and power allocation, a key question is how to optimally allocate resources such as channels to users. Previous studies have discussed user pairing schemes and power allocation algorithms for NOMA systems, but the key issue is how to allocate the channels. Coherent Ising Machine (CIM) is an Ising computer that can solve NP-hard combinatorial optimization problems at high speed. CIM can run optimization algorithms based on mutually coupled neural networks and can be applied to a variety of optimization problems. In this paper, we proposed a CIM-based optimization method for user pairing and channel allocation in NOMA systems. Simulation results show that the CIM-based optimization can achieve superior performance of the NOMA system.