Resistivity and anisotropic magnetization of single crystalline $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ La--Nd, Sm, Gd--Dy)*

We present a detailed study of $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ La--Nd, Sm, Gd--Dy) single crystals by measurements of temperature dependent magnetic susceptibility, magnetization, and electrical resistivity. The isostructural compounds \textit{RT}Bi$_{2}$ and \textit{RT}Sb$_{\mathrm{2}}$ are known to have widths of formation, except for $T =$ Ag. The $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ series forms with partial Ni occupancy as well as a variable Bi occupancy. For R $=$ Ce--Nd, Gd--Dy, the $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ compounds show local-moment-like behavior and order antiferromagnetically at low temperatures. Determination of anisotropies as well as antiferromagnetic ordering temperatures for $R$Ni$_{\mathrm{1-x}}$Bi$_{\mathrm{2\pm y}}$ (R $=$ Ce--Nd, Sm, Gd--Dy) have been made. Although crystalline samples from this family exhibit minority, second phase, superconductivity at low temperatures associated with Ni-Bi and Bi contamination, no evidence of bulk superconductivity has been observed.