Transporting suspended payloads is challenging for autonomous aerial vehicles because the payload can cause significant and unpredictable changes to the robot's dynamics. These changes can lead to suboptimal flight performance or even catastrophic failure. Although adaptive control and learning-based methods can in principle adapt to changes in these hybrid robot-payload systems, rapid mid-flight adaptation to payloads that have a priori unknown physical properties remains an open problem. We propose a meta-learning approach that learns how to adapt models of altered dynamics within seconds after picking up or dropping a payload. Our experiments demonstrate that our approach outperforms non-adaptive methods on several challenging suspended payload transportation tasks.