An algorithm for the simultaneous determination of two coefficients in an inverse problem for equations of the parabolic type is presented. The model under investigation has been proposed in the literature to describe the long-time coastal profile evolution. The iterative inversion procedure is based on the minimization of a suitable cost functional. Such a functional is considered in terms of the Laplace transforms of the solution to the original dynamical problem. Results of numerical tests are also shown to illustrate the performance of the algorithm.