  In the context of the factorization method, we investigate the pseudo-
Hermitian coherent states and its Hermitian counterpart coherent states under
the generalized quantum condition in the framework of a position-dependent
mass. By considering a specific modification in the superpotential, a suitable
annihilation and creation operators are constructed in order to reproduce the
Hermitian counterpart Hamiltonian in the factorized form. We show that by means
of these ladder operators we can construct a wide kind of exactly solvable
potentials as well as their accompanying coherent states. Alternatively, we
explore the relationship between the pseudo-Hermitian Hamiltonian and its
Hermitian counterparts, obtained from a similarity transformation, to construct
the associated pseudo-Hermitian coherent states. These latter preserve the
structure of Perelomov's states and minimize the generalized position-momentum
uncertainty principal.
