For pt.I see ibid., vol.21, p.3165 (1988). The density-functional theory of freezing is extended to the case of binary mixtures of hard discs viewed as a simple model for monolayers adsorbed on a smooth substrate. The theory is applied to the fluid-disordered crystal transition. The results are similar to those already obtained for the three-dimensional case: when the ratio of diameters is lowered, the phase diagram changes rapidly from a spindle, over a lower azeotrope to an eutectic diagram. Evidence is also found for the existence of a two-dimensional analogue of the empirical Hume-Rothery rule.