Color-octet quarkonia production .2.

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 (Q) over bar[S-1(0)(8)] and Q (Q) over bar[P-3(J)(8)] states hadronize into psi(Q) quarkonia at the same order in the NRQCD velocity expansion as previously considered Q (Q) over bar[S-3(1)(8)] pairs. Their contributions to prompt psi and Upsilon production at the Fermilab 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 (Q) over bar[S-1(0)(8)] and Q (Q) over bar[P-3(J)(8)] long distance matrix elements which can be extracted from the data are generally consistent with NRQCD scaling rules.