  Three linearly independent Hermitian invariants for the nonstationary
generalized singular oscillator (SO) are constructed and their complex linear
combination is diagonalized. The constructed family of eigenstates contains as
subsets all previously obtained solutions for the SO and includes all Robertson
and Schr\"odinger intelligent states for the three invariants. It is shown that
the constructed analogues of the SU(1,1) group-related coherent states for the
SO minimize the Robertson and Schr\"odinger relations for the three invariants
and for every pair of them simultaneously. The squeezing properties of the new
states are briefly discussed.
