  We present a scenario that ameliorates the tuning problems present in models
of primordial black hole dark matter from inflation. Our setup employs the
advantages of gravitational collapse in a long epoch of early matter domination
with reheating temperature $\lesssim 10^{6}~\text{GeV}$. Furthermore, we make
use of a string-inspired class of models where the inflaton is identified with
a non-compact axion field. In this framework, the presence of multiple local
minima in the inflaton potential can be traced back to an approximate discrete
shift symmetry. This scenario allows the formation of primordial black holes in
the observationally viable range of masses ($M_{\text{PBH}}\sim
10^{-13}M_{\odot}-10^{-16}M_{\odot}$) accounting for all dark matter, and in
excellent agreement with the CMB. Crucially, we find a significant reduction in
the required tuning of the parameters of the inflationary potential, in
contrast to the standard case of primordial black hole formation during
radiation domination. However, abundant formation of light PBHs during an early
phase of matter domination can be more easily in conflict with evaporation
bounds. We discuss how these can be avoided under mild assumptions on the
collapsing energy density fraction.
