  In this paper we consider a nonlinear generalization of the isotonic
oscillator in the same spirit as one considers the generalization of the
harmonic oscillator with a truly nonlinear restoring force. The corresponding
potential being asymmetric we invoke the symmetrization principle and construct
a symmetric potential in which the period function has the same value as in the
original asymmetric potential. The period function is amplitude dependent and
expressible in terms of the hypergeometric function and reduces to $2\pi$ when
$\alpha=1$, i.e., corresponding to the special case of an isotonic oscillator.
