  Possible anisotropic spin singlet pairings in Bi$_2$X$_3$ (X is Se or Te) are
studied. Among six pairings compatible with the crystal symmetry, two novel
pairings show nontrivial surface Andreev bound states, which form flat bands
and could produce zero bias conductance peak in measurements like point contact
spectroscopy. By considering purely repulsive short range Coulomb interaction
as the pairing mechanism, the dominant superexchange terms are all
antiferromagnetic, which would usually favor spin singlet pairing in
Bi$_2$X$_3$. Mean field analyses show that the interorbital pairing interaction
favors a mixed spatial-parity anisotropic pairing state, and one pairing
channel with zero energy surface states has a sizable component. The results
provide important new information for future experiments.
