Recently, distributed sustainable data centers based on renewable power generators have been deployed in order to efficiently reduce both the energy cost and carbon emission. Dynamic right-sizing (DRS) and frequency scaling (FS) have been considered as promising solutions to tune the computing capacity corresponding to the dynamic renewable power capacity. However, in existing works, the inaccurate power prediction and the uncoordinated decision making of DRS/FS still lead to low service quality and high energy cost. In this paper, we propose a novel joint optimization method for energy efficiently distributed sustainable data centers. The proposed method adopts long short-term memory approach to improve the prediction accuracy of renewable power capacity for a long period, and unsupervised deep learning (DL) solver to resolve the coordinated DRS/FS optimization. Furthermore, we present the MACRO/MICRO (MAMI) time scale-based data center management technique to achieve both high energy efficiency and low wake-up transition overhead of DRS. To evaluate the proposed DL-based MAMI optimizer, we use the real trace data of renewable power capacity from the U.S. Measurement and Instrumentation Data Center. The experimental results demonstrate that our method reduces the energy cost by 25% compared with conventional metaheuristics while guaranteeing the service response delay requirement.