Computer-simulation techniques are applied to analyze the late-stage ordering kinetics of a two-dimensional annealed dilute Ising model quenched into regions of its phase diagram that involve phase separation of phases with different densities. The order parameter of the model is a nonconserved quantity, whereas the global density is conserved. The ordered phases of the model are fourfold degenerate (2×1) and (2×2) superstructures on a square lattice. The equilibrium phase diagram involves a region of coexisting (2×1) and (2×2) phases and a region where the (2×2) phase coexists together with a gas phase. The results of the study show that the phase-separation kinetics in all cases are consistent with the Lifshitz-Slyozov growth law, R»(t)t1/3, where R»(t) is the characteristic linear domain size. These results are in agreement with recent low-energy electron-diffraction studies of the phase-separation kinetics in O/W(110) systems at high coverage.