The generalized Enskog theory of a hard-disk fluid is solved by a kinetic model method. Time correlation functions of the conserved variables of density, longitudinal and transverse current, and energy density are evaluated. The theoretical results are tested against molecular dynamics data at a density roughly half the solidification density. The good agreement obtained indicates that a kinetic equation which ignores correlated collisions can provide an adequate description of space-time correlations at finite wavelengths and frequencies in dense fluids in two dimensions.