  We introduce new generalized $q$-deformed coherent states ($q$-CS) by
replacing the $q$-factorial of $[n]_q!$ in the series expansion of the
classical $q$-CS by the generalized factorial $x_n^{q,\alpha}!$ where
$x_n^{q,\alpha}=(1+\alpha q^{n-1})[n]_q$. We use the shifted operators method
based on the sequence $x_n^{q,\alpha}$ to obtain a realization in terms of
Al-Salam-Chihara polynomials for the basis vectors of the Fock space carrying
the constructed $q$-CS. These new states interpolate between the $q$-CS of
Arik-Coon type ($\alpha=0$, $0<q<1$) and a set of coherent states of
Barut-Girardello type for the Meixner-Pollaczek oscillator ($\alpha\neq 0$,
$q\to 1$). We also discus their associated Bargmann type transforms.
