A theory for spin waves in diluted uniaxial antiferromagnets with random interactions in both exchange and single-ion anisotropy has been developed by extending a recent work on the related ferromagnets. As in the paper for the ferromagnets, the kind of coherent potential approximation (CPA) the authors consider here taking into account the dynamical effects of fluctuations in the exchange and local-anisotropy fields on the same level. For a two-sublattice antiferromagnet, however, the effective medium is self-consistently determined in terms of three parameters which, after using the time-reversal symmetry into the usual CPA T matrix condition for a pair of nearest-neighbour sites, may be reduced to only two independent parameters in the whole energy space. The concentration dependence, at zero temperature, of the zero-field antiferromagnetic resonance (or, equivalently, of the antiferromagnetic-'spin-flop' critical field) is analysed as a function of a local-anisotropy parameter and of the relative size of the anisotropy in the pure magnetic system. For systems with random non-competitive anisotropy, it is found that the general behaviour of these quantities with dilution is very much more sensitive to changes in both the random and non-random parts of the anisotropy than predicted by virtual-crystal approximation.