International society has a consensus to reduce carbon emissions and promote the development of low carbon economy in order to face the challenges of climate change. Achieving these goals depends not only on the production of low carbonization, but also on the consumption of low carbonization. The marketing strategy choice of enterprises is often greatly influenced by consumers' preference to low-carbon products. Facing the unknown consumer preference to low-carbon products, there is a great sense of marketing collaboration for manufacturers and retailers. Thus, the research on the marketing collaboration of low-carbon product supply chain has great realistic significance. In a low-carbon economy, some studies tried to resolve the optimization problems for the upstream supply chain in terms of production and operation. However, those studies were rarely able to do so from the perspective of marketing low-carbon products. Considering the impact of low-carbon goodwill on profit, this paper tries to explore the long-term marketing cooperation problem of the low-carbon product supply chain system consisted of a single manufacturer and a single retailer by using differential games. This study investigates the optimal marketing strategies of the manufacturer and retailer by adapting to the Nash non-cooperative game, Stackelberg leader-follower game and coordinated cooperative game, respectively. Subsequently, the equilibrium outcomes in the three game structures are comparatively analyzed. This study further discusses the dynamic coordination mechanism of low-carbon product supply chain marketing cooperation. This study aims to promote low-carbon consumption and reduce carbon emissions by optimizing the marketing decision mechanism. The first section proposes hypotheses and a general description of our proposed model. In the second section, considering the impact of low-carbon goodwill on profit, differential game models of the manufacturer and retailer are built respectively in the Nash non-cooperative game, Stackelberg leader-follower game and coordinated cooperative game. Each optimal equilibrium outcome is found by deducing the corresponding Hamilton-Jacobi-Bellman equation. In the third section, the equilibrium outcomes in the three game structures are comparatively analyzed. The results show that the supply chain's profit, the marketing efforts, and profit of both parties involved in the coordinated game are superior to those in the non-cooperative game. The fourth section discusses the range of distribution coefficients of supply chain's total profit to achieve Pareto optimality of individual profits of the manufacturer and retailer. Thus, the dynamic coordination mechanism of low-carbon product supply chain marketing cooperation is obtained. At last, the model is analyzed and confirmed with an example. To sum up, this paper expounds the value of long-term stable marketing cooperation for low-carbon product supply chain. On this basis, the dynamic coordination mechanism of supply chain marketing cooperation is discussed, and the range of distribution coefficients of supply chain's total profit is obtained. The paper provides a novel way for future research.