We investigate the ionic Hubbard model on a triangular lattice at three-quarters filling. This model displays a subtle interplay between metallic and insulating phases and between charge and magnetic orders. We find crossovers among Mott, charge transfer and covalent insulators, and magnetic order with large moments that persist even when the charge transfer is weak. Our theoretical results are consistent with experiments on A(0.5)CoO(2) (A=K,Na) and identify these materials as correlated covalent insulators.