To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d-wave and extended s-wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite-q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account.