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Diamond optomechanical crystal (OMC) devices with embedded color center spins are promising platforms for a broad range of applications in quantum sensing, networking, and computing, offering an interface between a GHz-frequency mechanical mode and both optical photons and coherent spins. A crucial but elusive step toward realizing this platform is to engineer a device with a high-quality factor mechanical mode while preserving the bulk-like coherence of embedded spins. Here, we demonstrate sideband-resolved diamond OMCs with mechanical quality factors in excess of 10⁶at cryogenic temperatures and find coherence times up toT₂=227µs for embedded nitrogen-vacancy (NV) centers. Furthermore, we measure these devices across five orders of magnitude in intracavity optical power, demonstrating robust power handling and a high optomechanical cooperativity (C≫1) at cryogenic temperatures, which is essential for a broad range of quantum protocols requiring strong, coherent interactions between photons and phonons. These results are enabled by a robust, high-throughput method for forming single-crystal diamond membranes in combination with chemical vapor deposition (CVD) diamond overgrowth with nitrogenδ-doping. We discuss the prospects of this platform for hybrid spin-mechanical devices in the quantum regime.