  Supersymmetry is a technique that allows us to extract information about the
states and spectra of quantum mechanical systems which may otherwise be
unsolvable. In this paper we reconstruct Ioffe's set of states for the singular
non-separable two-dimensional Morse potential using supersymmetry from a
non-degenerate set of states constructed for the initial separable Morse
Hamiltonian. We define generalised coherent states, compute their uncertainty
relations, and we find that the singularity in the partner Hamiltonian
significantly affects the localisation of the coherent state wavefunction.
