  Consider a general circle packing $\mathcal{P}$ in the complex plane
$\mathbb{C}$ invariant under a Kleinian group $\Gamma$. When $\Gamma$ is
convex-cocompact or its critical exponent is greater than 1, we obtain an
effective equidistribution for small circles in $\mathcal{P}$ intersecting any
bounded connected regular set in $\mathbb{C}$; this provides an effective
version of an earlier work of Oh-Shah. In view of the recent result of
McMullen-Mohammadi-Oh, our effective circle counting theorem applies to the
circles contained in the limit set of a convex-cocompact but non-cocompact
Kleinian group whose limit set contains at least one circle. Moreover consider
the circle packing $\mathcal{P}(\mathcal{T})$ of the ideal triangle attained by
filling in largest inner circles. We give an effective estimate to the number
of disks whose hyperbolic areas are greater than $t$, as $t\to 0$,
effectivising the work of Oh.
