  Motivated by recent experiments on SrCu$_2$(BO$_3$)$_2$, we investigate the
ground states of the doped Mott insulator on the Shastry-Sutherland lattice. To
provide a unified theoretical framework for both the valence-bond solid state
found in undoped SrCu$_2$(BO$_3$)$_2$ and the doped counterpart being pursued
in on-going experiments, we analyze the t-J-$V$ model via the bond operator
formulation. It is found that novel superconducting states emerge upon doping
with their properties crucially depending on the underlying valence bond order.
Implications to future experiments are discussed.
