Three new quaternary noncentrosymmetric sulfides, and () have been synthesized by a high-temperature solid-state method and flux growth method. The crystal structures of the compounds have been determined by single crystal X-ray diffraction. All compounds are isostructural and crystallize in the structure type and the cubic space group I ͞43d (No. 220) with unit cell parameters of a ​= ​14.308 ​Å (()), a ​= ​14.299 (2) Å (()), and a ​= ​14.336 (2) Å (()). The structure demonstrates good structural flexibility of mixing occupancy between Cu and X (X ​= ​Mg, Mn, Cd) at the Wyckoff site 12a. The structure consists of a distorted 3-dimensional framework constructed by (Cu/X) and tetrahedra. The divalent metals doped into the structure tune the band gaps of the compounds and contribute to good Second Harmonic Generation (SHG) response and high Laser Damage Threshold (LDT).