The effect of cluster Co-X-6 (X = S, N, O, and F) doping on the structural, electronic, magnetic, and optical properties of monolayer WS2 were studied by using the first-principles methods, and the results were compared with those in TM-X-6 (TM = Mn and Fe, X = S, N, O, and F) doped monolayer ZS(2) (Z = Mo and W) alloys from the references. All the formation energies under the W-rich condition were smaller than those under the S-rich condition. The Co-O-6 doped monolayer WS2 alloy was the most stable one among cluster Co-X-6 doped WS2 alloys. All cluster Co-X-6 (X = S, N, O, and F) doped monolayer WS2 alloys became magnetic HM which can be used in spintronic devices, but only portion of other TM-X-6 doped ZS(2) alloys were HM although they all were magnetic. The photoresponse of the cluster Co-X-6 (X = S, N, O, and F) doped monolayer WS2 alloys was enhanced due to the decrease of the band gaps. Although the cluster Co-X-6 (X = S, N, O, and F) doped monolayer WS2 alloys have been produced in the laboratory, we hope our study can offer some reference for the experiments.