After our first discovery of superconductivity (SC) with $T_C$=3.7 K in TlNi$_2$Se$_2$, we grew successfully a series of TlNi$_2$Se$_{2-x}$S$_x$ (0.0 $leq$ x $leq$2.0) single crystals. The measurements of resistivity, susceptibility and specific heat were carried out. We found that SC with $T_C$=2.3 K also emerges in TlNi$_2$S$_2$ crystal, which appears to involve heavy electrons with an effective mass $m^*$=13$sim$25 $m_b$, as inferred from the normal state electronic specific heat and the upper critical field, $H_{C2}(T)$. It was found that the $T_C$ and superconducting volume fraction in TlNi$_2$Se$_{2-x}$S$_x$ crystals changes with the disorder degree induced by the partial substitution of S for Se, which is characterized by the residual resistivity ratio (textit{RRR}). The effect of the disorder on SC may provide some information for understanding the mechanism of SC in this new Ni-chalcogenide system.
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