  The self-annihilation of dark matter particles with mass in the MeV range can
produce gamma rays via prompt or secondary radiation. The annihilation rate for
such light dark matter particles is however tightly constrained by cosmic
microwave background (CMB) data. Here we explore the possibility of discovering
MeV dark matter annihilation with future MeV gamma-ray telescopes taking into
account the latest and future CMB constraints. We study the optimal energy
window as a function of the dominant annihilation final state. We consider both
the (conservative) case of the dwarf spheroidal galaxy Draco and the (more
optimistic) case of the Galactic center. We find that for certain channels,
including those with one or two monochromatic photon(s) and one or two neutral
pion(s), a detectable gamma-ray signal is possible for both targets under
consideration, and compatible with CMB constraints. For other annihilation
channels, however, including all leptonic annihilation channels and two charged
pions, CMB data rule out any significant signal of dark matter annihilation at
future MeV gamma-ray telescopes from dwarf galaxies, but possibly not for the
Galactic center.
