A coherent-potential-approximation (CPA) formalism for the treatment of III-V quaternary semiconductor alloys with two disordered sublattices is developed. This formalism is applied to the alloys AlxGa1-xAsyP1-y, AlxGa1-xAsySb1-y, In1-xGaxAsyP1-y, and In1-xGaxAsySb1-y, and results are presented for the CPA densities of states, self-energies, band-bowing parameters, and energy-gap variations with composition. Deviations from the virtual-crystal approximation (VCA), which are indications of the effects of alloy disorder, are found to be more significant for the alloys In1-xGaxAsySb1-y and In1-xGaxAsyP1-y than for AlxGa1-xAsyP1-y and AlxGa1-xAsySb1-y. As expected, the amount of disorder as measured by the magnitudes of the self-energy shifts, bowings, and differences between the CPA and VCA energy gaps is stronger at certain alloy compositions than others. Comparison is also made of the experimental energy gap of In1-xGaxAsyP1-y lattice matched to InP, with calculated VCA and CPA energy gaps.