  Primordial black holes (PBHs), formed out of large overdensities in the early
Universe, are a viable dark matter (DM) candidate over a broad range of masses.
Ultra-light, asteroid-mass PBHs with masses around $10^{17}$ g are particularly
interesting as current observations allow them to constitute the entire DM
density. PBHs in this mass range emit $\sim$ MeV photons via Hawking radiation
which can directly be detected by the gamma ray telescopes, such as the
upcoming AMEGO. In this work we forecast how well an instrument with the
sensitivity of AMEGO will be able to detect, or rule out, PBHs as a DM
candidate, by searching for their evaporating signature when marginalizing over
the Galactic and extra-Galactic gamma-ray backgrounds. We find that an
instrument with the sensitivity of AMEGO could exclude non-rotating PBHs as the
only DM component for masses up to $7 \times 10^{17}$ g at 95% confidence level
(C.L.) for a monochromatic mass distribution, improving upon current bounds by
nearly an order of magnitude. The forecasted constraints are more stringent for
PBHs that have rotation, or which follow extended mass distributions.
