Temporal Graph Neural Networks (TGNNs) are widely used to model dynamic systems where relationships and features evolve over time. Although TGNNs demonstrate strong predictive capabilities in these domains, their complex architectures pose significant challenges for explainability. Counterfactual explanation methods provide a promising solution by illustrating how modifications to input graphs can influence model predictions. To address this challenge, we present CoDy—Counterfactual Explainer for Dynamic Graphs—a model-agnostic, instance-level explanation approach that identifies counterfactual subgraphs to interpret TGNN predictions. CoDy employs a search algorithm that combines Monte Carlo Tree Search with heuristic selection policies, efficiently exploring a vast search space of potential explanatory subgraphs by leveraging spatial, temporal, and local event impact information. Extensive experiments against state-of-the-art factual and counterfactual baselines demonstrate CoDy's effectiveness, with improvements of 16% in AUFSC+ over the strongest baseline. Our code is available at: https://github.com/daniel-gomm/CoDy