  For the oscillator-like systems, connected with q-Hermite polynomials,
coherent states of Barut-Girardello type are defined. The well-known Arik-Coon
oscillator naturally arose in the framework of suggested approach as
oscillator, connected with the Rogers q-Hermite polynomials, in the same way as
usual oscillator with standard Hermite polynomials. The results about the
coherent states for discrete q-Hermite polynomials of II type are quite new.
