  We present results of a numerical analysis of magnon spectra in supercells
simulating two-dimensional and bulk random diluted ferromagnets with
long-ranged pair exchange interactions. We show that low-energy spectral
regions for these strongly disordered systems contain a coherent component
leading to interference phenomena manifested by a pronounced sensitivity of the
lowest excitation energies to the adopted boundary conditions. The dependence
of configuration averages of these excitation energies on the supercell size
can be used for an efficient determination of the spin-wave stiffness D. The
developed formalism is applied to the ferromagnetic Mn-doped GaAs semiconductor
with optional incorporation of phosphorus; the obtained concentration trends of
D are found in reasonable agreement with recent experiments. Moreover, a
relation of the spin stiffness to the Curie temperature Tc has been studied for
Mn-doped GaAs and GaN semiconductors. It is found that the ratio Tc/D exhibits
qualitatively the same dependence on Mn concentration in both systems.
