In light of increasingly prominent environmental issues, inspiring green supply chain (GSC) members to engage in collaborative innovation is crucial to improve environmental performance. In this paper, in relation to a two-level GSC consisting of manufacturers and suppliers, differential equations involving the greenness of intermediate and final products as state variables are constructed considering the effect of digital capability on green innovation. Subsequently, designs for three incentive mechanisms—the greenness reward, the R&D effort reward, and the digital construction reward—are presented, and their long-term dynamic effects on the economic, environmental, and social benefits are compared and analyzed. Finally, the impacts of consumer green preference and the contribution of digital capability to the advancement of green innovation are explored. The findings show that all these incentives can boost economic, environmental, and social benefits while motivating the supplier. To achieve the best incentive effect, the reward coefficient should fall within a specific range. The digital construction reward mechanism is the most favourable in the initial stage, while the R&D effort reward mechanism is the most appropriate in the long term. The promotion effects of digital capability on green innovation and consumer green preference have the potential to enhance economic, environmental, and social performance.