In explainable AI, a prominent approach is to explain the predictions of a classifier (such as a Neural Network) using counterfactuals (CFs), namely instances resulting from perturbations that lead to a change of the classification label. We propose to demonstrate a prototype system called CoDeC, which computes CF-based explanations for a given classifier and prediction. Uniquely, CoDeC computes a diverse set of CFs that adhere to denial constraints, which are defined with respect to a database of instances. These constraints may be mined from e.g. a training set, and/or manually crafted. They are then intuitively used to guide the generation of realistic CFs. The implementation is based on combining a previously proposed solution for finding diverse CFs (DiCE) with an iterative approach that first looks for CFs while disregarding the constraints, then looks for tuples in the proximity of the obtained CFs that further satisfy the constraints, and repeats the process if necessary. We will demonstrate CoDeC in the context of explanations for neural models trained and deployed with respect to the Adult Income and NY-housing datasets.