  We construct a new family of q-deformed coherent states $|z>_q$, where $0 < q
< 1$. These states are normalizable on the whole complex plane and continuous
in their label $z$. They allow the resolution of unity in the form of an
ordinary integral with a positive weight function obtained through the analytic
solution of the associated Stieltjes power-moment problem and expressed in
terms of one of the two Jacksons's $q$-exponentials. They also permit exact
evaluation of matrix elements of physically-relevant operators. We use this to
show that the photon number statistics for the states is sub-Poissonian and
that they exhibit quadrature squeezing as well as an enhanced signal-to-quantum
noise ratio over the conventional coherent state value. Finally, we establish
that they are the eigenstates of some deformed boson annihilation operator and
study some of their characteristics in deformed quantum optics.
