Over time, many leading organizations have started to include Corporate Social Responsibility as an instrument to enhance their brand image, and gain competitive advantage. In this paper, we develop a game-theoretic Stackelberg model for a two-periodic socially responsible supply chain with cost-learning capabilities. We study both the revenue sharing and wholesale price contracts under various permutations to achieve supply chain coordination. In the process, we use analytical, numerical, and graphical methods to understand how the contract parameters affect the channel partner's performance under two-periodic setting. The results show that although the wholesale price contract fails to solve double marginalization, interestingly, the combination of the wholesale price and revenue sharing contracts can coordinate a two-period socially responsible supply chain, but fails to resolve the channel conflict. However, the revenue sharing contract does resolve the channel conflicts under two-periodic setting.