  For a time-dependent harmonic oscillator with an inverse squared singular
term, we find the generalized invariant using the Lie algebra of $SU(2)$ and
construct the number-type eigenstates and the coherent states using the
spectrum-generating Lie algebra of $SU(1,1)$. We obtain the evolution operator
in both of the Lie algebras. The number-type eigenstates and the coherent
states are constructed group-theoretically for both the time-independent and
the time-dependent harmonic oscillators with the singular term. It is shown
that the squeeze operator transforms unitarily the time-dependent basis of the
spectrum-generating Lie algebra of $SU(1,1)$ for the generalized invariant, and
thereby evolves the initial vacuum into a final coherent vacuum.
