Governments' energy-saving emission reduction policies and consumers' low-carbon preference have important implications for an enterprise's production operations. Implementing processes that save energy and reduce carbon emissions always increases a company's operation costs. In response to the consumers who has low-carbon preference, companies often adopt advertising campaigns to increase product sales, which further increases the sales cost. The increase of production and sale costs bring down the market performance of supply chain. In this paper, a low-carbon supply chain channel with one manufacturer and one retailer is considered and how to optimize the low-carbon supply chain management decision is shown and the supply chain performance is improved through contract design. In this paper the co-op advertising (CA) contract and the co-op advertising and emission reduction cost sharing (CA-ERCS) contracts how to impact the low-carbon supply chain's optimal decision and coordination are analyzed. How the optimal decision and coordination change when a retailer has fairness concerns is also explored. There are several findings. First, regardless of whether or not the retailer has fairness concerns, a co-op advertising contract cannot achieve channel coordination, but can enhance channel effectiveness; Second, when the retailer does not have fairness concerns, the co-op advertising and emission reduction cost sharing contracts can achieve channel coordination and achieve win-win situation under certain conditions; Third, the retailer's fairness concerns can change the co-op advertising and emission reduction cost sharing contracts' coordination in some cases:when the retailer feels general equality, the channel can be coordinated; when the retailer feels disadvantageous inequality, the channel can be coordinated only when the marginal profits of the manufacturer and the retailer within a certain proportion; but when the retailer feels advantageous inequality, the channel cannot be coordinated. So the retailer's fairness concerns can change the contract's coordination under certain conditions. Our study contributes to the theoretical basis for the design of low-carbon supply chain cooperation contracts, especially in cases where the retailer has fairness concerns.