We derive two multivariate generating functions for three-dimensional
Young diagrams (also called plane partitions). The variables
correspond to a colouring of the boxes according to a finite Abelian
subgroup G of SO(3). We use the vertex operator methods of
Okounkov--Reshetikhin--Vafa for the easy case G = Z/n; to handle the
considerably more difficult case G=Z/2 x Z/2, we will also use a
refinement of the author's recent q--enumeration of pyramid
partitions. In the appendix, we relate the diagram generating
functions to the Donaldson-Thomas partition functions of the orbifold
C^3/G. We find a relationship between the Donaldson-Thomas partition
functions of the orbifold and its G-Hilbert scheme resolution. We
formulate a crepant resolution conjecture for the Donaldson-Thomas
theory of local orbifolds satisfying the Hard Lefschetz condition.