  Motivated by the recent discovery of superconductivity in layered
Na$_{x}$CoO$_{2}\cdot y$H$_{2}$O compound, we investigate theoretically the
spin dynamics in the superconducting state with three possible $p_{x}+ip_{y}$-,
$d+id'$-, and $f$-wave pairing symmetries in two-dimensional triangular
lattices. We find that a spin resonance peak, which is elaborated to have a
close relevance to the relative phase of the gap function and the geometry of
the Fermi surface, appears in both in-plane and out-of-plane components of the
spin susceptibility $\chi$ for the spin-singlet $d+id'$-wave pairing, while
only in the out-of-plane(in-plane) component of $\chi$ for the spin-triplet
$p_{x}+ip_{y}$-wave ($f$-wave) pairing. Because the pairing symmetry in this
compound is still hotly debated at present, this distinct feature may be used
to probe or determine it unambiguously with future neutron scattering
experiments.
