  We present the effective $J$-factors for the Milky Way for scenarios in which
dark matter annihilation is p-wave or d-wave suppressed. We find that the
velocity suppression of dark matter annihilation can have a sizable effect on
the morphology of a potential dark matter annihilation signal in the Galactic
Center. The gamma-ray flux from the innermost region of the Galactic Center is
in particular suppressed. We find that for dark matter density profiles with
steep inner slopes, the morphology of the Inner Galaxy gamma-ray emission in
p-wave models can be made similar to the morphology in standard s-wave models.
This similarity may suggest that model discrimination between s-wave and p-wave
is challenging, for example, when fitting the Galactic Center excess. However,
we show that it is difficult to simultaneously match s- and p-wave morphologies
at both large and small angular scales. The $J$-factors we calculate may be
implemented with astrophysical foreground models to self-consistently determine
the morphology of the excess with velocity-suppressed dark matter annihilation.
