We report the structural and magnetic properties of RNi (R = Dy, Tb1/3Dy1/3Ho1/3, and Gd1/5Tb1/5Dy1/5Ho1/5Er1/5) to investigate the high-entropy effect at the rare-earth site. The lattice parameters are almost unchanged by the increase of configurational entropy, which is due to the successive partial substitution of Dy by a pair of rare earth elements located on both sides of Dy in the Periodic Table. All compounds exhibit ferromagnetic ground states. The replacement of Dy with Tb + Ho, which does not have magnetic interactions in competition with Dy, does not affect the magnetic ordering temperature. Although (Gd1/5Tb1/5Dy1/5Ho1/5Er1/5)Ni shows the Curie temperature close to that of DyNi, an additional magnetic anomaly, which would be a spin reorientation, is observed probably due to the introduction of competing magnetic interactions between R = Gd and Er compounds and R = Tb, Dy, and Ho ones. We have also assessed the magnetocaloric effect, and the configurational entropy dependence of the magnetic entropy change reflects that of the temperature derivative of the magnetic susceptibility. Our analysis suggests the possibility of enhancing magnetocaloric properties by designing the anisotropy of rare-earth magnetic moments in the high-entropy state.