  This paper is a natural continuation of the previous paper J.Phys. A:
Math.Theor. 44 (2011) 425204, arXiv 0907.1736 [quant-ph] where oscillator
representations for nonnegative Calogero Hamiltonians with coupling constant
$\alpha\geq-1/4$ were constructed. Here, we present generalized oscillator
representations for all Calogero Hamiltonians with $\alpha\geq-1/4$.These
representations are generally highly nonunique, but there exists an optimum
representation for each Hamiltonian.
