Autonomous underwater vehicles (AUVs) are underwater robotic platforms used in a variety of applications. An AUV's navigation solution relies heavily on the fusion of inertial sensors and Doppler velocity logs (DVL), where the latter delivers accurate velocity updates. To ensure accurate navigation, a DVL calibration is undertaken before the mission begins to estimate its error terms. During calibration, the AUV follows a complex trajectory and employs nonlinear estimation filters to estimate error terms. In this paper, we introduce DCNet, a data-driven framework that utilizes a two-dimensional convolution kernel in an innovative way. Using DCNet and our proposed DVL error model, we offer a rapid calibration procedure. This can be applied to a trajectory with a nearly constant velocity. To train and test our proposed approach a dataset of 276 minutes long with real DVL recorded measurements was used. We demonstrated an average improvement of 70% in accuracy and 80% improvement in calibration time, compared to the baseline approach, with a low-performance DVL. As a result of those improvements, an AUV employing a low-cost DVL, can achieve higher accuracy, shorter calibration time, and apply a simple nearly constant velocity calibration trajectory. Our results also open up new applications for marine robotics utilizing low-cost, high-accurate DVLs.