Solid ion conductors exhibit a frequency dependent conductivity that is well described by the coupling model, which includes stretched-exponential relaxation to describe ion-ion interactions. As yet, materials characterization taking this frequency dependence into account is inaccessible to non-experts in numerical analysis, since it requires computer-assisted evaluation of complex integrals. On the other hand, commonly used impedance models lead to inaccurate results and have limited applicability. The purpose of this article is to provide an approximation to the coupling model in terms of elemental functions. With fits to multiple reference data sets we demonstrate the advantages of our approach over commonly used methods. We then apply our model to the characterization of polyethylene oxide based electrolytes, used in all-solid-state batteries, and show that such a case could not be accurately studied with standard impedance models.