To stimulate the capital-constrained manufacturer to produce green products, the government often adopts two incentive mechanisms: green credit (i.e., subsidy offered directly to bank) and subsidy (i.e., subsidy offered directly to manufacturer). This paper examines the optimal interest rate of the bank, and the optimal product green degree and sales price of the manufacturer under the two mechanisms, respectively. Furthermore, we investigate the effects of these mechanisms on the optimal decisions, the profits of players, the social welfare and the environmental benefits. Several important results are obtained. First, when the total government subsidy is low, the green credit mechanism can bring the higher green degree, product sales price and demand, as well as higher profits for the bank and manufacturer, rather than the subsidy mechanism. Otherwise, the result is opposite. Second, the government should adopt the green credit mechanism to support the manufacturer to develop green products when the budget is limited and relatively low. If the government budget is sufficient, the subsidy mechanism is the best choice, which can bring higher economic and environmental benefits.