  Meixner oscillators have a ground state and an `energy' spectrum that is
equally spaced; they are a two-parameter family of models that satisfy a
Hamiltonian equation with a {\it difference} operator. Meixner oscillators
include as limits and particular cases the Charlier, Kravchuk and Hermite
(common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson
transformation they are also related with a relativistic model of the linear
harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and
their continuous weight function. We construct explicitly the corresponding
coherent states with the dynamical symmetry group Sp(2,$\Re$). The reproducing
kernel for the wavefunctions of these models is also found.
