  The coherent state method has proved to be useful in quantum physics and
mathematics. This method, more precisely, the vector coherent state method, has
been used by some authors to construct representations of superalgebras but
almost, to our knowledge, it has not yet been extended to quantum
superalgebras, except $U_q[osp(1|2)]$, one of the smallest quantum
superalgebras. In this article the method is applied to a bigger quantum
superalgebra, namely $U_q[gl(2|1)]$, in constructing $q$--boson-fermion
realizations and finite-dimensional representations which, when irreducible,
are classified into typical and nontypical representations. This construction
leads to a more general class of $q$--boson-fermion realizations and
finite-dimensional representations of $U_q[gl(2|1)]$ and, thus, at $q=1$, of
$gl(2|1)$. Both $gl(2|1)$ and $U_q[gl(2|1)]$ have found different physics
applications, therefore, it is meaningful to construct their representations.
