  We discuss neutral Higgs boson production through gluon fusion and
bottom-quark annihilation in the CP-conserving $\mathbb{Z}_3$-invariant
Next-to-Minimal Supersymmetric Standard Model (NMSSM) at proton colliders. For
gluon fusion we adapt known asymptotic expansions in supersymmetric particles
for the inclusion of next-to-leading order contributions of squarks and gluinos
from the Minimal Supersymmetric Standard Model (MSSM) and include electro-weak
corrections involving light quarks. Together with the resummation of higher
order sbottom contributions in the bottom-quark Yukawa coupling for both
production processes we thus present accurate cross section predictions
implemented in a new release of the code SusHi. We elaborate on the new
features of an additional SU$(2)_L$ singlet in the production of CP-even and
-odd Higgs bosons with respect to the MSSM and include a short discussion of
theory uncertainties.
