  The aim of this paper is to introduce a general way to stabilize the
perturbative QCD computations of heavy quarkonium production in the boosted or
high-momentum transferring region with tree-level generators only. Such an
approach is possible by properly taking into account the power-enhanced
perturbative contributions in a soft and collinear safe manner without
requiring any complete higher-order computations. The complicated NLO results
for inclusive quarkonium hadroproduction can be well reproduced within our
approach based on a tree-level generator {\sc\small HELAC-Onia}. We have
applied it to estimate the last missing leading-twist contribution from the
spin-triplet color-singlet S-wave production at $\mathcal{O}(\alpha_s^5)$,
which is a NNLO term in the $\alpha_s$ expansion for the quarkonium $P_T$
spectrum. We conclude that the missing NNLO contribution will not change the
order of the magnitude of the short-distance coefficient. Such an approach is
also quite appealing as it foresees broad applications in quarkonium-associated
production processes, which are mostly absent of complete higher-order
computations and fragmentation functions.
