  A Sierpi\'nski packing in the $2$-sphere is a countable collection of
disjoint, non-separating continua with diameters shrinking to zero. We show
that any Sierpi\'nski packing by continua whose diameters are square-summable
can be uniformized by a disk packing with a packing-conformal map, a notion
that generalizes conformality in open sets. Being special cases of Sierpi\'nski
packings, Sierpi\'nski carpets and some domains and can be uniformized by disk
packings as well. As a corollary of the main result, the conformal loop
ensemble (CLE) carpets can be uniformized conformally by disk packings,
answering a question of Rohde-Werness.
