  We consider ADHM instantons in product group gauge theories that arise from
D3-branes located at points in the orbifold R^6/Z_p. At finite N we argue that
the ADHM construction and collective coordinate integration measure can be
deduced from the dynamics of D-instantons in the D3-brane background. For the
large-N conformal field theories of this type, we compute a saddle-point
approximation of the ADHM integration measure and show that it is proportional
to the partition function of D-instantons in the dual AdS_5 x S^5/Z_p
background, in agreement with the orbifold AdS/CFT correspondence. Matching the
expected behaviour of D-instantons, we find that when S^5/Z_p is smooth a
saddle-point solution only exists in the sector where the instanton charges in
each gauge group factor are the same. However, when S^5/Z_p is singular, the
instanton charges at large N need not be the same and the space of saddle-point
solutions has a number of distinct branches which represent the possible
fractionations of D-instantons at the singularity. For the theories with a type
0B dual the saddle-point solutions manifest two types of D-instantons.
