Non-orthogonal multiple access (NOMA) technique is important for achieving a high data rate in next-generation wireless communications. A key challenge to fully utilizing the effectiveness of the NOMA technique is the optimization of the resource allocation (RA), e.g., channel and power. However, this RA optimization problem is NP-hard, and obtaining a good approximation of a solution with a low computational complexity algorithm is not easy. To overcome this problem, we propose the coherent Ising machine (CIM) based optimization method for channel allocation in NOMA systems. The CIM is an Ising system that can deliver fair approximate solutions to combinatorial optimization problems at high speed (millisecond order) by operating optimization algorithms based on mutually connected photonic neural networks. The performance of our proposed method was evaluated using a simulation model of the CIM. We compared the performance of our proposed method to simulated annealing, a conventional-NOMA pairing scheme, deep Q learning based scheme, and an exhaustive search scheme. Simulation results indicate that our proposed method is superior in terms of speed and the attained optimal solutions.