This study establishes a low-carbon construction supply chain (CSC) composed of a developer and a contractor. The developer invests in low-carbon promotion (LCP) to give consumers more accurate information about the project's low-carbon aspects. The contractor invests in low-carbon construction technology (LCT) with the intention of reducing carbon emissions. This paper explores the investment strategies and cooperative behaviors of developers and contractors from the perspective of government subsidies and further studies the conditions that affect the successful implementation of cost-sharing contracts between the developer and contractor. This study considers four decision-making scenarios: decentralized decision-making without government subsidies, decentralized decision-making with government subsidies, unilateral cost-sharing contract (UCC) with government subsidies, and bilateral cost-sharing contract (BCC) with government subsidies. The findings indicate that: (1) The contractor's LCT investment has a better optimization effect on CSC than the developer's LCP investment. (2) When only government subsidies are implemented, subsidizing contractors is more conducive to the optimization of CSC. When UCC and BCC are further introduced, subsidizing developers becomes more beneficial. Moreover, excessively high subsidy standards are not conducive to the sustainable development of CSC. (3) UCC and BCC both hold the potential for Pareto improvements within CSC, with success contingent upon specific conditions, and BCC tends to achieve better optimization than UCC. (4) The marginal profits of developers and contractors primarily drive the effectiveness of contracts. CSC's sustainability is jeopardized by cost-sharing ratios that are either excessively high or too low. This study provides a robust theoretical foundation for promoting low-carbon cooperation among members of CSC and formulating government subsidy policies.