Sleep stage classifiers monitoring the wakefulness level of resting-state fMRI recordings have been proposed by several studies; however, the application of deep learning methods remains largely unexplored. We investigated the performance of Convolutional Neural Networks (CNNs) in the classification of sleep stages using fMRI-derived dynamic Functional Connectivity (dFC) features and simultaneous EEG-based labels. All tested architectures exhibited accuracies above 80%, with the best performance achieved using a shallow network. The learned filter weights were coherent with known stage-specific patterns of thalamo-cortical dFC. CNNs yielded comparable classification accuracy to Support Vector Machines (SVMs), without the need for exhaustive hyperparameter tuning.