Resting-state functional MRI (rsfMRI) yields functional connectomes that can serve as cognitive fingerprints of individuals. Connectomic fingerprints have proven useful in many machine learning tasks, such as predicting subject-specific behavioral traits or task-evoked activity. In this work, we propose a surface-based convolutional neural network (BrainSurfCNN) model to predict individual task contrasts from their resting-state fingerprints. We introduce a reconstructive-contrastive loss that enforces subject-specificity of model outputs while minimizing predictive error. The proposed approach significantly improves the accuracy of predicted contrasts over a well-established baseline. Furthermore, BrainSurfCNN's prediction also surpasses test-retest benchmark in a subject identification task.