<p>Existing studies on coal-power supply chain coordination under cap-and-trade mainly assume deterministic carbon prices and relatively simple contract structures, leaving the joint design of operational coordination and carbon-price risk allocation under stochastic permit prices largely unexplored. This paper studies a two-echelon coal-power supply chain regulated by cap-and-trade when the carbon price is stochastic. Demand is linear and each tier can reduce its emission factor through costly abatement. We first derive closed-form Stackelberg equilibria under decentralised decision-making and the closed-form centralised system optimum as a benchmark. Under risk neutrality, carbon-price volatility does not change the optimal quantity or abatement decisions, but it magnifies profit risk through the chain’s net carbon position. We then propose a hybrid contract that combines net carbon position sharing with a two-part tariff. The contract coordinates the decentralised chain to the centralised benchmark and enables a full range of Pareto-improving profit allocations. To capture risk aversion, we further develop a distributionally robust mean-variance framework with a bounded carbon-price variance. The centralised policy trades off expected profit against exposure to carbon-price uncertainty, and the hybrid contract can implement this policy while sharing risk between members. Numerical experiments illustrate how the mean and volatility of carbon prices, abatement efficiencies, and allowance endowments shape decisions, risk sharing, and profits, and we discuss managerial implications for supply chains operating under carbon markets.</p>