This paper presents a novel method based on a Hybrid Multi-Objective Evolutionary strategy for the automatic design of a lightweight convolutional neural network used for coronary stenosis classification. The hybrid methodology consists of two search stages, starting with the Multi-Objective Evolutionary Algorithm based on Decomposition, to generate a set of optimal solutions focused on the minimization of two objectives: the accuracy classification error and the number of learning parameters in the convolutional neural network. Subsequently, the Simulated Annealing algorithm is applied to improve a subset of the solutions produced in the previous step. After the method was complete, a convolutional neural network model consisting of 3498 learning parameters was found by the proposed hybrid strategy, which is a considerably low number compared with the other architectures reported in the literature. Consequently, the found model achieved the highest classification performance rate in terms of the Accuracy and Jaccard Similarity Coefficient metrics with values of $0.94$ and $0.89$, respectively, using a database consisting of 608 images of regions with positive and negative coronary stenosis cases. On a second test, the model was tested using a database consisting of 2788 instances of natural and synthetic images of coronary stenosis cases. Corresponding maximum classification rates of $0.97$ and $0.93$ for the Accuracy and Jaccard Similarity Coefficient metrics, respectively, were achieved. In addition, the average required time to classify a single instance was $0.009$ seconds. The obtained results showed that the proposed method is feasible for the automatic design of lightweight convolutional neural networks that can be used as a part of decision-making systems in clinical practice.