We calculate the lowest order hadronic cross sections for producing colored heavy quark-antiquark pairs in $L=S=0$ and $L=S=1$ configurations. Such $Q\Qbar[{}^1S_0^{(8)}]$ and $Q\Qbar[{}^3P_J^{(8)}]$ states hadronize into $��_\Q$ quarkonia at the same order in the NRQCD velocity expansion as previously considered $Q\Qbar[{}^3S_1^{(8)}]$ pairs. Their contributions to prompt Psi and Upsilon production at the Tevatron bring the shapes of theoretical transverse momentum distributions into line with recent CDF measurements. We find that the best fit values for the linear combinations of $Q\Qbar[{}^1S_0^{(8)}]$ and $Q\Qbar[{}^3P_J^{(8)}]$ long distance matrix elements which can be extracted from the data are generally consistent with NRQCD scaling rules.

27 pages, harvmac, 9 uuencoded figures. Section in original version of this article which discussed quarkonia spin alignment has been removed