[en] Layered Co oxide Na_xCoO₂·yH₂O with a superconducting transition temperature T_c=4.5 K has been studied by ⁵⁹Co NQR. The nuclear spin relaxation rate 1/⁵⁹T₁ is nearly proportional to temperature T in the normal state. In the superconducting state, it exhibits the coherence peak and decreases with decreasing T below ∼0.8T_c. Detailed comparison of the 1/T₁T values and the magnetic susceptibilities between Na_xCoO₂·yH₂O and Na_xCoO₂ implies that the metallic state of the former system is closer to a ferromagnetic phase than that of the latter. These experimental results impose a restriction on the mechanism of the superconductivity. (author)