This research introduces an algorithm that automatically detects five primary emotions in individuals with Down syndrome: happiness, anger, sadness, surprise, and neutrality. The study was conducted in a specialized institution dedicated to caring for individuals with Down syndrome, which allowed for collecting samples in uncontrolled environments and capturing spontaneous emotions. Collecting samples through facial images strictly followed a protocol approved by certified Ethics Committees in Ecuador and Colombia. The proposed system consists of three convolutional neural networks (CNNs). The first network analyzes facial microexpressions by assessing the intensity of action units associated with each emotion. The second network utilizes transfer learning based on the mini-Xception architecture, using the Dataset-DS, comprising images collected from individuals with Down syndrome as the validation dataset. Finally, these two networks are combined in a CNN network to enhance accuracy. The final CNN processes the information, resulting in an accuracy of 85.30% in emotion recognition. In addition, the algorithm was optimized by tuning specific hyperparameters of the network, leading to a 91.48% accuracy in emotion recognition accuracy, specifically for people with Down syndrome.