Accurate trajectory prediction and motion planning are crucial for autonomous driving systems to navigate safely in complex, interactive environments characterized by multimodal uncertainties. However, current generation-then-evaluation frameworks typically construct multiple plausible trajectory hypotheses but ultimately adopt a single most likely outcome, leading to overconfident decisions and a lack of fallback strategies that are vital for safety in rare but critical scenarios. Moreover, the usual decoupling of prediction and planning modules could result in socially inconsistent or unrealistic joint trajectories, especially in highly interactive traffic. To address these challenges, we propose a contingency-aware diffusion planner (CoPlanner), a unified framework that jointly models multi-agent interactive trajectory generation and contingency-aware motion planning. Specifically, the pivot-conditioned diffusion mechanism anchors trajectory sampling on a validated, shared short-term segment to preserve temporal consistency, while stochastically generating diverse long-horizon branches that capture multimodal motion evolutions. In parallel, we design a contingency-aware multi-scenario scoring strategy that evaluates candidate ego trajectories across multiple plausible long-horizon evolution scenarios, balancing safety, progress, and comfort. This integrated design preserves feasible fallback options and enhances robustness under uncertainty, leading to more realistic interaction-aware planning. Extensive closed-loop experiments on the nuPlan benchmark demonstrate that CoPlanner consistently surpasses state-of-the-art methods on both Val14 and Test14 datasets, achieving significant improvements in safety and comfort under both reactive and non-reactive settings. Code and model will be made publicly available upon acceptance.