In this study, we attempted to classify categorical emotional states using Electrodermal Activity (EDA) signals and a configurable Convolutional Neural Network (cCNN). The EDA signals from the publicly available, Continuously Annotated Signals of Emotion dataset were down-sampled and decomposed into phasic components using the cvxEDA algorithm. The phasic component of EDA was subjected to Short-Time Fourier Transform-based time-frequency representation to obtain spectrograms. These spectrograms were input to the proposed cCNN to automatically learn the prominent features and discriminate varied emotions such as amusing, boring, relaxing, and scary. Nested k-Fold cross-validation was used to evaluate the robustness of the model. The results indicated that the proposed pipeline could discriminate the considered emotional states with a high average classification accuracy, recall, specificity, precision, and F-measure scores of 80.20%, 60.41%, 86.8%, 60.05%, and 58.61%, respectively. Thus, the proposed pipeline could be valuable in examining diverse emotional states in normal and clinical conditions.