  We present, for the isospectral family of oscillator Hamiltonians, a
systematic procedure for constructing raising and lowering operators satisfying
any prescribed `distorted' Heisenberg algebra (including the
$q$-generalization). This is done by means of an operator transformation
implemented by a shift operator. The latter is obtained by solving an
appropriate partial isometry condition in the Hilbert space. Formal
representations of the non-local operators concerned are given in terms of
pseudo-differential operators. Using the new annihilation operators, new
classes of coherent states are constructed for isospectral oscillator
Hamiltonians. The corresponding Fock-Bargmann representations are also
considered, with specific reference to the order of the entire function family
in each case.
