  As a model of a novel superconductor Na_xCoO_2\cdotyH_2O, a single-band t-J
model on a triangular lattice is studied, using a variational Monte Carlo
method. We calculate the energies of various superconducting (SC) states,
changing the doping rate \delta and sign of t for small J/|t|. Symmetries of s,
d, and d+id (p+ip and f) waves are taken up as candidates for singlet (triplet)
pairing. In addition, the possibility of Nagaoka ferromagnetism and
inhomogeneous phases is considered. It is revealed that, among the SC states,
the d+id wave always has the lowest energy, which result supports previous
mean-field studies. There is no possibility of triplet pairing, although the
f-wave state becomes stable against a normal state in a special case
(\delta=0.5 and t<0). For t<0, the complete ferromagnetic state is dominant in
a wide range of \delta and J/|t|, which covers the realistic parameter region
of superconductivity.
