Through density functional theory (DFT) calculations, a new triclinic monolayer, namely CoBiS, with higher stability than that of penta-CoBiS, is predicted. Our results show that this monolayer is a nonmagnetic metallic compound. To tune its magnetic properties, we systematically investigated the formation and energetics of different point defects in the CoBiS monolayer, such as VBi, VS and VCo. We find that the monolayer becomes magnetic with the different points defects. Our calculated magnetic anisotropy energy (MAE) indicated that VBi and VS exhibit out-of-plane MAE, while the MAE is in-plane for VCo. By solving the Heisenberg model using the Monte Carlo simulation method, we obtain transition temperatures for VS and VCo systems much larger than room temperature, implying potential applications in spintronic devices.