  Canonical coherent states can be written as infinite series in powers of a
single complex number $z$ and a positive integer $\rho(m)$. The requirement
that these states realize a resolution of the identity typically results in a
moment problem, where the moments form the positive sequence of real numbers
$\{\rho(m)\}_{m=0}^\infty$. In this paper we obtain new classes of vector
coherent states by simultaneously replacing the complex number $z$ and the
moments $\rho(m)$ of the canonical coherent states by $n \times n$ matrices.
Associated oscillator algebras are discussed with the aid of a generalized
matrix factorial. Two physical examples are discussed. In the first example
coherent states are obtained for the Jaynes-Cummings model in the weak coupling
limit and some physical properties are discussed in terms of the constructed
coherent states. In the second example coherent states are obtained for a
conditionally exactly solvable supersymmetric radial harmonic oscillator.
