  We discuss the double spin asymmetries in charmonium hadroproduction with
nonzero transverse momenta at fixed target energies, $\sqrt{s}\simeq40$ GeV,
within the framework of the factorization approach. It is shown that the color
octet contribution is dominant in the asymmetries. The size of the asymmetries
and the projected statistical errors in a future option of HERA with
longitudinally polarized protons scattering off a polarized target (HERA-$\vec
N$) should allow to distinguish between different parametrizations for the
polarized gluon distribution in the proton.
