  This paper is a natural continuation of the previous paper \cite{TyuVo13}
where generalized oscillator representations for Calogero Hamiltonians with
potential $V(x)=\alpha/x^2$, $\alpha\geq-1/4$, were constructed. In this paper,
we present generalized oscillator representations for all generalized Calogero
Hamiltonians with potential $V(x)=g_{1}/x^2+g_{2}x^2$, $g_{1}\geq-1/4$,
$g_{2}>0$. These representations are generally highly nonunique, but there
exists an optimum representation for each Hamiltonian, representation that
explicitly determines the ground state and the ground-state energy. For
generalized Calogero Hamiltonians with coupling constants $g_1<-1/4$ or
$g_2<0$, generalized oscillator representations do not exist in agreement with
the fact that the respective Hamiltonians are not bounded from below.
