Carbon neutrality requires joint efforts of the society. Consumer subsidy is an important way to spread the concept of green consumption and support industrial green transformation. Point-based green consumption reward programs being piloted in many cities is a greenness subsidy scheme. Under this new subsidy scheme, the amount of subsidy is calculated based on the greenness of the product consumed - the greener the product is, the higher the subsidy is. This is different from the traditional lump-sum subsidy scheme where the government determines the amount of subsidy that is not related to the greenness of product. This paper constructs a game-theoretic model with endogenized green product development and pricing decisions. We propose the optimal subsidy strategies under lump-sum and greenness subsidy schemes, and compare their economic and environmental consequences. The study finds that both schemes can encourage firms to exert more efforts in green product development, and greenness subsidy is effective in more contexts. When optimizing a subsidy scheme, one should pay attention to the fact that consumer subsidies can increase carbon emissions by stimulating overconsumption, and a large market size and strong consumer preference for green products can help eliminate this side effect. From the perspective of scheme selection, when the government budget is extremely low or high, the greenness subsidy is superior in terms of carbon reduction; when the budget is moderate, the lump-sum subsidy scheme with a proper subsidy standard can achieve higher emission reduction. The above conclusions can provide theoretical support for the government in designing green consumption subsidy schemes.