  We report the anomalous breakdown in the scaling of the microscopic magnetic
susceptibility, as measured via the ${}^{31}$P nuclear magnetic resonance (NMR)
shift $K$, with the bulk magnetic susceptibility $\chi$ in the paramagnetic
state of Mn$_2$P$_2$S$_6$. This anomaly occurs near $T_\mathrm{max} \sim 117$ K
the maximum in $\chi(T)$ and is therefore associated with the onset of
quasi-two-dimensional (quasi-2D) magnetic correlations. The spin-lattice
relaxation rate divided by temperature $(T_1T)^{-1}$ in Mn$_2$P$_2$S$_6$
exhibits broad peak-like behavior as a function of temperature, qualitatively
following $\chi$, but displaying no evidence of critical slowing down above the
N\'{e}el temperature $T_N$. In the magnetic state of Mn$_2$P$_2$S$_6$, NMR
spectra provide good evidence for 60 degree rotation of stacking-fault-induced
magnetic domains, as well as observation of the spin-flop transition that
onsets at 4 T. The temperature-dependent critical behavior of the internal
hyperfine field at the P site in Mn$_2$P$_2$S$_6$ is consistent with previous
measurements and the two-dimensional anisotropic Heisenberg model. In a sample
of Ni$_2$P$_2$S$_6$, we observe only two magnetically split resonances in the
magnetic state, demonstrating that the multiple-peaked NMR spectra previously
associated with 60 degree rotation of stacking faults is sample dependent.
Finally, we report the observation of a spin-flop-induced splitting of the NMR
spectra in Ni$_2$P$_2$S$_6$, with an onset spin-flop field of $H_\mathrm{sf} =
14$ T.
