  We study exclusive charmonium production in diffractive deep inelastic
scattering and ultra-peripheral heavy-ion collisions within the dipole picture.
The mass spectrum and light-front wavefunctions of charmonium are obtained from
the basis light-front quantization approach, using the one-gluon exchange
interaction plus a confining potential inspired by light-front holography. We
apply these light-front wavefunctions to exclusive charmonium production. The
resulting cross sections are in reasonable agreement with electron-proton
collision data at HERA and ultra-peripheral nucleus collision measurements at
RHIC and LHC. The charmonium cross-section has model dependence on the dipole
model. We observe that the cross-section ratio of excited states to the ground
state has a weaker dependence than the cross-section itself. We suggest that
measurements of excited states of heavy quarkonium production in future
electron-ion collision experiments will impose rigorous constraints on heavy
quarkonium light-front wavefunctions, thus improving our understanding of meson
structure, which eventually will help us develop a precise description of the
gluon distribution function in the small-$x$ regime.
