  A notion of asymptotically conical K\"ahler orbifold is introduced, and,
following previous existence results in the setting of asymptotically conical
manifolds, it is shown that a certain complex Monge-Amp\'ere equation admits a
rapidly decaying solution (which is unique for certain intervals of decay
rates), allowing one to construct K\"ahler metrics with prescribed Ricci forms.
In particular, if the orbifold has trivial canonical bundle, then Ricci-flat
metrics can be constructed, provided certain additional hypotheses are met.
This implies for example that orbifold crepant partial resolutions of varieties
associated to Calabi-Yau cones admit a one-parameter family of Calabi-Yau
metrics in each K\"ahler class that contains positive (1,1)-forms.
