Symmetry in spectrum space of isotonic oscillators is studied, and a distinct fi gure is given by appropriate parametric substitution. An analytic expression of normalized eigenfunction is obtained. It is proven that linear oscillator is a degeneration of isotonic oscillator. It is revealed that an isotonic oscillator is a two_photon parametric model. Coherent state of that model is given, and that coherent state includes odd_coherent state and even_coherent state constru cted by Glauber coherent states in a natural way.