  We study pumping of magnons to the Dirac points of magnon's Brillouin zone of
a ferromagnet on a honeycomb lattice. In particular, we consider second-order
Suhl process, when due to interaction between magnons, a pair of magnons is
created due to absorption of two electromagnetic wave quanta. We introduce a
bosonic analog of the Cooper ladder for the magnon pair, which is shown to
enhance the pairing of magnons at the Dirac points. As a result of pairing of
the Dirac magnons, the system becomes unstable towards formation of a magnetic
state with zero or reduced magnetization - the Dirac magnon paired state. In
this case the resonant frequency of the pump equals to that of energy of the
Dirac points. Our estimates suggest that the Dirac magnon paired state can be
found in the CrBr$_{3}$ or CrCl$_{3}$ ferromagnet below in vicinity of the
Curie temperature.
