A construction of Gaussian Klauder coherent states for systems with degenerate energy spectra is presented. Of special interest are the cases of truly accidental degeneracy that do not arise from a hidden or explicit symmetry. This is the case for a particle in a two-dimensional square box. In this case, the degeneracy results from the number of different ways an integer can be expressed as the sum of two squares. It is shown how to manage this situation and produce generalized coherent states that can mimic classical particle behavior for many collisions with the box walls.