  We consider the $4d$ $\mathcal{N}=2$ superconformal quiver gauge theory
obtained by a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ super Yang-Mills
(SYM). By exploiting supersymmetric localization, we study the integrated
correlator of two Coulomb branch and two moment map operators and the
integrated correlator of four moment map operators, determining exact
expressions valid for any value of the 't Hooft coupling in the planar limit.
Additionally, for the second correlator, we obtain an exact expression also for
the next-to-planar contribution. Then, we derive the leading terms of their
strong-coupling expansions and outline the differences with respect to the
$\mathcal{N}=4$ SYM theory.
