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Impurity effects on the triangular antiferromagnets Ni$_{1-x}M_x$Ga$_2$S$_4$ ($M=$ Mn, Fe, Co and Zn) are studied. The 2D frozen spin-disordered state of NiGa$_2$S$_4$ is stable against the substitution of Zn$^{2+}$ ($S=0$) and Heisenberg Fe$^{2+}$ ($S=2$) spins, and exhibits a $T^2$-dependent magnetic specific heat, scaled by the Weiss temperature. In contrast, the substitutions with Co$^{2+}$ ($S=3/2$) spin with Ising-like anisotropy and Heisenberg Mn$^{2+}$ ($S=5/2$) spin induce a conventional spin glass phase. From these comparisons, it is suggested that integer size of Heisenberg spins is important to stabilize the 2D coherent behavior observed in the frozen spin-disordered state.