  In this paper we construct coherent states for the two-dimensional Morse
potential. We find the dependence of the spectrum on the physical parameters
and use this to understand the emergence of accidental degeneracies. It is
observed that, under certain conditions pertaining to the irrationality of the
parameters, accidental degeneracies do not appear and as such energy levels are
at most two-fold degenerate. After defining a non-degenerate spectrum and set
of states for the 2D Morse potential, we construct generalised coherent states
and discuss the spatial distribution of their probability densities and their
uncertainty relations.
