Super resolution (SR) is a promising approach for improving the quality of low resolution steaming services on mobile devices.On mobile devices, the available computing and memory resources change dynamically depending on other running applications.Due to the high computation and memory demands of SR models, it is essential to adapt the model according to available resources to harvest the best possible model performance while maintaining quality of service (QoS), such as meeting a minimum framerate and avoiding interruptions. Nevertheless, there is no SR model or machine learning system that supports adaptive SR, and enabling adaptive SR model on mobile devices is challenging because adapting model can cause significant framerate drop or even service interruption. To address this challenge, we take an algorithm and system co-design approach and propose DySR that maintains QoS while maximizing the model performance. During the training stage, DySR employs an adaption-aware one-shot Neural Architecture Search to produce sub-graphs that share kernel operation weights for low model adaption overhead while striking a balance between performance and framerate. During the inference stage, an incremental model adaption method is developed for further reducing the model adaption overhead. We evaluate on a diverse set of hardware and datasets to show that DySR can generate models close to the Pareto frontier while maintaining a steady framerate throughput with a memory footprint of around 40\% less compared to baseline methods.