To perform dynamic cable manipulation to realize the configuration specified by a target image, we formulate dynamic cable manipulation as a stochastic forward model. Then, we propose a method to handle uncertainty by maximizing the expectation, which also considers estimation errors of the trained model. To avoid issues like multiple local minima and requirement of differentiability by gradient-based methods, we propose using a black-box optimization (BBO) to optimize joint angles to realize a goal image. Among BBO, we use the Tree-structured Parzen Estimator (TPE), a type of Bayesian optimization. By incorporating constraints into the TPE, the optimized joint angles are constrained within the range of motion. Since TPE is population-based, it is better able to detect multiple feasible configurations using the estimated inverse model. We evaluated image similarity between the target and cable images captured by executing the robot using optimal transport distance. The results show that the proposed method improves accuracy compared to conventional gradient-based approaches and methods that use deterministic models that do not consider uncertainty.