We demonstrate fabrication methods for micro-/nanoelectromechanical systems (MEMS/NEMS) in single-crystal diamond chip. Such devices can be used to study embedded color centers, such as the nitrogen vacancy (NV) or the silicon vacancy (SiV). Color centers have discrete electronic and spin energy levels, which can be controlled by engineering the amount of strain in the diamond lattice. These strain fields can be effectively controlled using conventional MEMS/NEMS devices. As a specific demonstration, we show the tuning of SiV electronic energy levels via static actuation. The device design process accounting for various fundamental and experimental constraints is discussed.