  Based on an effective Hamiltonian with the binary alloy disorder model
defined in the triangular lattice, the impurity scattering effects on the
density of states and especially on the spin-lattice relaxation rate $1/T_1$ of
$p_x+ip_y$-wave superconductors are studied by solving numerically the
Bogoliubov-de Gennes equations. In the clean limit, the coherence peak of
$1/T_1$ is observed as expected. More intriguingly, for strong scattering
potential, the temperature dependence of $1/T_1$ exhibits the two different
power law behaviors near $T_{\text{c}}$ and at low temperatures, respectively,
which is in good agreement with the nuclear quadrupolar resonance measurement.
