  We propose a generalized su(2) algebra that perfectly describes the discrete
energy part of the Morse potential. Then, we examine particular examples and
the approach can be applied to any Morse oscillator and to practically any
physical system whose spectrum is finite. Further, we construct the Klauder
coherent state for Morse potential satisfying the resolution of identity with a
positive measure, obtained through the solution of truncated Stieltjes moment
problem. The time evolution of the uncertainty relation of the constructed
coherent states is analyzed. The uncertainty relation is more localized for
small values of radius of convergence.
