  By using the constrained-phase quantum Monte Carlo method, we performed a
systematic study of the pairing correlations in the ground state of the doped
Kane-Mele-Hubbard model on a honeycomb lattice. We find that pairing
correlations with $d+id$ symmetry dominate close to half filling, but pairing
correlations with $p+ip$ symmetry dominate as hole doping moves the system
below three-quarters filling. We correlate these behaviors of the pairing
correlations with the topology of the Fermi surfaces of the non-interacting
problem. We also find that the effective pairing correlation is enhanced
greatly as the interaction increases, and these superconducting correlations
are robust against varying the spin-orbit coupling strength. Our numerical
results suggest a possible way to realize spin triplet superconductivity in
doped honeycomb-like materials or ultracold atoms in optical traps.
