Under the rapid development of the global economy, environmental pollution has intensified significantly. The evolving external environment presents both opportunities and challenges to traditional supply chains. As an innovative management philosophy and practical approach, the green supply chain has rapidly become an integral component of corporate sustainable development strategies. However, the transition from traditional supply chain to green supply chain necessitates effective collaboration and coordination among supply chain members. Contractual coordination has therefore emerged as an effective methodology to enhance operational efficiency and profitability across supply chain participants. To investigate the impact of various coordination mechanisms on the optimal decision-making of green supply chains, we construct a Stackelberg game model involving bilateral green investments by both manufacturer and retailer within a two-echelon green supply chain system. Considering the bilateral green efforts from both manufacturer and retailer, we comparatively analyze game equilibrium solutions under three scenarios: non-coordination, cost-sharing contract coordination, and two-part contract coordination. Specifically，we examine how these coordination mechanisms influence pricing strategies, green investment levels, and profit distributions within the supply chain network. Finally, the results are validated and illustrated using numerical simulation. It is discovered that 1) the cost-sharing contract cannot simultaneously increase the Pareto improvement of producers' and retailers' revenues; 2) the cost-sharing contract cannot increase the social utility and additive greenness of products; however, it can improve the marketing effort; and 3) When retailers maintain an optimistic stance toward manufacturers' green initiatives, the two-part tariff contract enables concurrent Pareto improvements in both parties' profits while simultaneously enhancing product greenness, marketing efforts, and social welfare, thereby achieving efficient supply chain coordination.