Short-lag spatial coherence (SLSC) beamforming has the potential to improve the diagnostic power of a multitude of ultrasound imaging techniques. One challenge for advanced real-time implementation is repeated correlation calculations. To address this challenge, this paper introduces CohereNet - a novel deep neural network architecture that estimates the coherence function in efforts to bypass the repeated correlation calculations required for SLSC imaging. The network was trained and evaluated using in vivo breast data, demonstrating similar contrast, CNR, SNR, and GCNR with an average correlation between the original image and the DNN image of 0.93, and improved computational speed (i.e., a factor of 3.4 improvement) when compared to the offline implementations. In addition, the model is generalizable across multiple tissue types, probe geometries, and ultrasound systems. These results are promising for the use of deep learning architectures as a replacement for correlation estimation in multiple areas of coherence-based ultrasound imaging.