Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials

We are continuing here the study of generalized coherent states of Barut–Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete $q$-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.