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.