  We study inclusive heavy quarkonium production with definite polarizations in
polarized proton-proton collisions using the non-relativistic QCD color-octet
mechanism. We present results for rapidity distributions of cross sections and
spin asymmetries for the production of J/psi and psi' with specific
polarizations in polarized p-p collisions at \sqrt s = 200 GeV and 500 GeV at
the RHIC within the PHENIX detector acceptance range.
