Stacked intelligent metasurfaces (SIM) have become a promising technology to improve the wave-domain signal processing and increase the wireless communication capacity. However, optimizing the phase configuration remains a significant challenge due to the discrete and highly combinatorial nature of the multi-layer architecture. To address this, we propose a quantum-inspired coordinated design framework for joint wave-based beamforming and power allocation in SIM-assisted multiuser systems. By leveraging a black-box second-order approximation, the discrete phase optimization is reformulated into a standard quadratic unconstrained binary optimization (QUBO) problem. Quantum-inspired discrete simulated bifurcation (dSB) solver is used to find the candidates effectively, and then a tabu-based local refinement strategy is applied to refine these candidates and reduce the deviation of the approximate solution. Concurrently, an iterative water-filling scheme is integrated to optimize power allocation, facilitating a synergy between global search and fine-grained control. Simulation results confirm that the proposed approach consistently outperforms classical benchmarks in terms of sum rate, convergence speed, and interference suppression. The framework exhibits strong scalability across varying system dimensions and channel realizations, validating its effectiveness in wave-domain communication scenarios.