A phenomenological model, based on the generalized Langevin equation scheme first developed by Bruesch, Zeller, and co-workers, is employed to calculate the Raman band shapes for metal-halogen stretching modes in ionic conductors of the Ag2HgI4 class. The observed strong broadening of the Hg-I4 stretch mode near 122 cm-1 is explained as arising from coupling to the mobile ion diffusive mode. Below the β→α phase transition, the Ag-I mode is oscillatory, and the coupling effect is negligible on either Ag-I or Hg-I. In the conducting phase, the long time diffusive character of the Ag-I motion results in a strong effective damping of the Hg-I motion, leading to the observed broadening. The coupling effects are strong only when one of the two modes is indeed diffusive, thus explaining the apparent value of the Raman linewidth as a screening device for possible new ionic conductor crystals.