The paper studies how the combination of the manufacturer’s carbon emission reduction and the retailer’s emission reduction relevant promotion impacts the performances of a dyadic supply chain in low-carbon environment. We consider three typical scenarios, that is, centralized and decentralized without or with side-payment. We compare measures of supply chain performances, such as profitabilities, emission reduction efficiencies, and effectiveness, in these scenarios. To improve chain-wide performances, a new side-payment contract is designed to coordinate the supply chain and numerical experiments are also conducted. We find the following. (1) In decentralized setting, the retailer will provide emission cutting allowance to the manufacturer only if their unit product profit margin is higher enough than the manufacturer’s, and the emission reduction level of per unit product is a monotonically increasing function with respect to the cost pooling proportion provided by the retailer; (2) the new side-payment contract can coordinate the dyadic supply chain successfully due to its integrating sales promotion effort and emission reduction input, which results in system pareto optimality under decentralized individual rationality but achieves a collective rationality effect in the centralized setting; (3) when without external force’s regulation, consumers’ low-carbon awareness is to enhance consumers’ utility and decrease profits of supply chain firms.