Constraint Programming (CP) is a powerful paradigm for solving combinatorial problems, yet translating natural language problem descriptions into executable models remains a significant bottleneck. While Large Language Models (LLMs) show promise in automating this translation, they often struggle with subtle semantic errors in the absence of oracle validation at test time. To address this, we introduce CP-SynC (Constraint Programming modeling with Synthesized Checkers), a multi-agent workflow for zero-shot constraint modeling in MiniZinc. CP-SynC coordinates modeling agents that generate and refine candidate models and validation agents that synthesize semantic checkers to provide feedback on semantic correctness. To mitigate noise inherent in individual LLM outputs, CP-SynC explores multiple modeling trajectories in parallel and employs selection agents to select the final model via multi-agent evidence aggregation. Extensive experiments on a benchmark of 100 CP problems show that CP-SynC substantially outperforms existing baselines in MiniZinc modeling.