Reducing servers' power usage in data centers upon utility's request has been emerging as a valuable demand response resource for enhancing power grid's efficiency and reliability, especially during emergency events (e.g., extreme weather) that result in electricity production shortage and put the grid in jeopardy. Nonetheless, for demand response in multitenant colocation data centers, operators may have to leverage expensive and environmentally-unfriendly diesel generation, because individual tenants manage their own servers' power usage without coordination and are typically charged by data center operators based on fixed power contracts that provide no incentives for demand response. This paper focuses on emergency demand response (EDR) and proposes an auction-based incentive mechanism, called FairDR, that incentivizes and coordinates tenants' energy reduction through financial rewards for enabling cost-effective and low-carbon EDR in colocation data center. FairDR decides tenants' energy reduction online without knowing a priori the future energy reduction requirements. It is proved that FairDR ensures tenants' truthfulness in the auction process, attains a bounded overall cost saving compared to the offline optimum which knows all the demands, and guarantees fairness (i.e., similar rewards are offered if tenants reduce the same amount of energy) that is largely absent in the existing auction mechanisms. Finally, trace-driven simulations are performed to validate our analysis and demonstrate that FairDR outperforms the existing mechanisms by improving fairness and achieving a good cost saving that is comparable to the offline optimum.