  In the case of a one-dimensional nonsingular Hamiltonian $H$ and a singular
supersymmetric partner $H_a$, the Darboux and factorization relations of
supersymmetric quantum mechanics can be only formal relations. It was shown how
we can construct an adequate partner by using infinite barriers placed where
are located the singularities on the real axis and recover isospectrality. This
method was applied to superpartners of the harmonic oscillator with one
singularity. In this paper, we apply this method to the singular isotonic
oscillator with two singularities on the real axis. We also applied these
results to four 2D superintegrable systems with second and third-order
integrals of motion obtained by Gravel for which polynomial algebras approach
does not allow to obtain the energy spectrum of square integrable
wavefunctions. We obtain solutions involving parabolic cylinder functions.
