We consider a coal supply chain with a coal enterprise and a manufacturer, where the coal enterprise invests in clean coal technology, and the manufacturer invests in carbon reduction technology. The government offers subsidies for the investments of clean coal technology and carbon reduction technology. We examine optimal clean coal technology inputs in a coal enterprise and carbon reduction quantity in a manufacturer under the modes of coal-enterprise-led and manufacturer-led, respectively, using a Stackelberg game theory model. We obtain some interesting results. First, carbon reduction by the manufacturer is restrained when clean coal technology cost and carbon reduction cost are increased, regardless of the dominant modes, and clean coal technology input decreases when clean coal technology cost increases; however, a high carbon reduction cost has no effect on clean coal technology input when the manufacturer leads. Second, the clean coal technology subsidy for coal enterprises promotes clean coal technology inputs and carbon reductions, and the carbon reduction subsidy encourages carbon reduction without supporting clean coal technology input. Last, carbon reduction performance is better achieved under the manufacturer-led model than the coal-enterprise-led model. However, it should be noticed that the capital resource only relies on government subsidy in this article. In the future, this study could be used for green supply chain investment, and could be helpful for sustainability development.