  We study the hadro- and photo-production of $\bar cc$ and $\bar bb$ mesons at
low transverse momentum to high orders in the relative velocity of the pair, v,
in non-relativistic QCD. We evaluate cross sections to order v^7 for $\eta_c$,
sufficient for studies of photo-production in the almost-elastic region. For
all other charmonium states we find the cross section to order v^9, sufficient
for studies of the ratio of $\chi_{c1}$ and $\chi_{c2}$ production rates. We
find recurrence formulae for generating terms at even higher orders, should
they be needed.
