We present a kinetic Monte Carlo lattice gas model including top and bridge sites on a square lattice, with pairwise lateral interactions between the adsorbates. In addition to the pairwise lateral interactions we include an additional interaction: an adsorbate is forbidden to adsorb on a bridge site formed by two surface atoms when both surface atoms are already forming a bond with an adsorbate. This model is used to reproduce the low and high coverage adsorption behaviour of CO on Pt(100) and Rh(100). The parameter set used to simulate CO on Pt(100) produces the c(2 x 2)-2t ordered structure at 0.50 ML coverage, a one-dimensionally ordered structure similar to the experimentally observed (3 square root(2) x square root(2)) - 2t + 2b structure at 0.67 ML coverage, the c(4 x 2)-4t + 2b ordered structure at 0.75 ML coverage, and the recently reported c(6 x 2)-6t + 4b ordered structure at 0.83 ML coverage. The (5 square root(2) x square root(2)) ordered structure at 0.60 ML coverage is not reproduced by our model. The parameter set used to simulate CO on Rh(100) produces the c(2 x 2)-2t ordered structure at 0.50 ML coverage, a one-dimensionally ordered structure similar to the experimentally observed (4 square root(2) x square root(2)) - 2t + 4b structure at 0.75 ML coverage, and the c(6 x 2)-6t + 4b ordered structure at 0.83 ML coverage. Additionally, the simulated change of top and bridge site occupation as a function of coverage matches the trend in experimental vibrational peak intensities.