  In this paper we define a non-unitary displacement operator, which by acting
on the vacuum state of the pseudo harmonic oscillator (PHO), generates new
class of generalized coherent states (GCSs). An interesting feature of this
approach is that, contrary to the Klauder-Perelomov and Barut-Girardello
approaches, it does not require the existence of dynamical symmetries
associated with the system under consideration. These states admit a resolution
of the identity through positive definite measures on the complex plane. We
have shown that the realization of these states for different values of the
deformation parameters leads to the well-known Klauder-Perelomov and
Barut-Girardello CSs associated with the $su(1,1)$ Lie algebra. This is why we
call them the generalized $su(1,1)$ CSs for the PHO. Finally, study of some
statistical characters such as squeezing, anti-bunching effect and
sub-Poissonian statistics reveals that the constructed GCSs have indeed
nonclassical features.
