Deep learning has become the new state-of-the-art for many problems in image analysis. However, large datasets are often required for such deep networks to learn effectively. This poses a difficult challenge for many medical image analysis problems in which only a small number of subjects are available, e.g., patients undergoing a new treatment. In this work, we propose a number of approaches for learning generalizable recurrent neural networks from smaller task-fMRI datasets: 1) a resampling method for ROI-based fMRI analysis to create augmented data; 2) inclusion of a small number of non-imaging variables to provide subject-specific initialization of the recurrent neural network; and 3) selection of the most generalizable model from multiple reinitialized training runs using criteria based on only training loss. Using cross-validation to assess model performance, we demonstrate the effectiveness of the proposed methods to train recurrent neural networks from small datasets to predict treatment outcome for children with autism spectrum disorder (N = 21) and classify autistic vs. typical control subjects (N = 40) from task-fMRI scans.