  In this work we provide a first principles description of the electronic and
optical properties of bilayers C$_3$N, with different stacking motifs AB, AB$'$
and AA$'$. Starting from quasi-particle electronic band-structures, we solve
the Bethe Salpeter Equation (BSE) to access the excitonic properties of these
bilayers. For all stacking sequences, we see strong optical absorption at
energies lower than but close to that of the monolayer. Most relevant, we
predict a strong quenching of the low-energy optical absorption, with
negligible oscillator strength of low-lying bound excitons. This is a unique
phenomenology that does not arise in the monolayer case, nor in other common
homo-bilayers. We explain these findings in terms of the small interband dipole
matrix elements associated to the valence-conduction transitions involved in
these excitons, and discuss them in view of the different stacking motifs.
