This paper aims at designing coordination contract in a dual channel supply chain (DCSC) which consists of a socially responsible manufacturer and a retailer. We build stylized game models under both centralized and decentralized scenarios. Then, we identify the reason for supply chain inefficiency under decentralized scenario. Further, according to the manufacturer's corporate social responsibility (CSR) coefficient, we design two different contracts to achieve coordination. We find that with the impact of CSR, social welfare under centralized scenario is always higher than that under decentralized scenario. However, profit of the whole supply chain between the two scenarios has different relationship. More specifically, when CSR coefficient is relatively low, profit under centralized scenario is higher than that under decentralized scenario. When CSR coefficient is high, profit under centralized scenario is lower than that under decentralized scenario. Due to these two cases, we respectively design revenue sharing contract with franchise fee and wholesale price contract with franchise fee and government subsidy to achieve coordination. The result suggests that encouraging the manufacturer to bear CSR properly can reach a multi-win for social welfare, consumers and supply chain members through coordination contract. However, when CSR coefficient is higher than a certain threshold, conflict between supply chain members becomes irreconcilable which results in the retailer's resistance. In this condition, only through subsidy from government or philanthropic organization can supply chain members sustain their cooperation.