Summary: Green product development depends on the green innovation behavior of upstream and downstream companies in the supply chain. This paper focuses on a green supply chain consisting of a supplier and a manufacturer and considers two financing schemes wherein the manufacturer’s operating capital and green innovation capital are both constrained: bank credit financing (BCF) and supplier green investment (SGI). We investigate the financing strategy of a manufacturer with different financing decision preferences and supply chain coordination contract designs. The results show that when the manufacturer’s financing decision preference is low bankruptcy risk, it should choose BCF when the bank loan interest rate is lower than a threshold and SGI when the bank loan interest rate is higher than this threshold; when the manufacturer’s financing decision preference is high R&D benefit, it should choose BCF when the initial capital is lower than another threshold and choose SGI when the initial capital is higher than this threshold. Then, we compare whether cost-sharing, quantity discount and revenue-sharing contracts can coordinate the supply chain, and discuss the selection strategies of supply chain members for coordination contracts. Research shows that revenue-sharing contracts fail to coordinate; however, when the cost-sharing ratio and quantity discount rate are appropriate, both cost-sharing and quantity discount contracts can achieve supply chain coordination. The lower the supplier’s unit production cost, the stronger its motivation to accept a higher cost-sharing ratio and quantity discount rate. For the supplier, the key to choosing any coordination contract lies in the relative height of the cost-sharing ratio and quantity discount rate while the manufacturer should always choose a quantity discount contract when the quantity discount rate is high enough.