  Paramagnons are the collective modes that govern the spin response of nearly
magnetic conductors. In some cases they mediate electron pairing leading to
superconductivity. This scenario may occur in 2H-NbSe$_2$ monolayers, that
feature spin-valley coupling on account of spin-orbit interactions and their
lack of inversion symmetry. Here we explore spin anisotropy of paramagnons both
for non-centrosymmetric Kane-Mele-Hubbard models for 2H-NbSe$_2$ monolayers
described with a DFT-derived tight-binding model. In the infinite wavelength
limit we find spatially uniform paramagnons with energies around $1$~meV that
feature a colossal off-plane uniaxial magnetic anisotropy, with quenched
transversal spin response. At finite wave vectors, longitudinal and transverse
channels reverse roles: XY fluctuations dominate within a significant portion
of the Brillouin zone. Our results show that 2H-NbSe$_2$ is close to a
Coulomb-driven in-plane (XY) spin density wave instability.
