  Coy dark matter is an effective scheme in which a fermionic dark matter
candidate interacts with the Standard Model fermions via a pseudoscalar
mediator. This simple setup avoids the strong constraints posed by direct
detection experiments in a natural way and explains, on top of the observed
dark matter relic abundance, the spatially extended gamma-ray excess recently
detected at the Galactic Center. In this Letter we study the phenomenology of
coy dark matter accounting for a novel signature of the model: the diphoton
annihilation signal induced by the Standard Model fermions at the loop level.
By challenging the model with the observations of spheroidal dwarf satellite
galaxies and the results of gamma-ray line searches obtained by the Fermi LAT
experiment, we assess its compatibility with the measured dark matter relic
abundance and the Galactic Center excesses. We show that despite the gamma-ray
line constraint rules out a significant fraction of the considered parameter
space, the region connected to the observed Galactic Center excess remains
currently viable. Nevertheless, we find that next-generation experiments such
as DAMPE, HERD and GAMMA-400 have the potential to probe exhaustively this
elusive scenario.
