  The possibility of multiple phase diagram in the novel superconductor
Na_{x}CoO_{2}yH_{2}O is analyzed on the basis of the multi-orbital Hubbard
model including the atomic spin-orbit coupling. We have shown that the spin
triplet pairing state is stable in this model. The p-wave (f-wave) state is
stabilized when the Hund's rule coupling is large (small). In the precedent
paper, we have determined the direction of d-vector at T=Tc and H=0 within the
linearized Dyson-Gorkov equation. In this paper, the pairing state below Tc and
under the magnetic field is determined within the weak coupling approximation
including the paramagnetic effect. We find that the p+f coexistent state is
stabilized at low temperatures in a part of parameter range. We point out that
the phase diagram in the H-T plane is quite different between the p-wave,
f-wave and p+f-wave superconductivities. The characteristics of each phase are
clarified by showing the magnetic susceptibility and specific heat. We discuss
the comparison with experimental results and suggest some future experiments to
detect the multiple phase transition.
