  We study D-instanton contributions to supergraviton scattering amplitudes in
the ten-dimensional type IIB superstring theory beyond the leading
non-perturbative order. In particular, we determine the one-D-instanton
contribution to maximal R-symmetry violating (MRV) amplitudes with arbitrary
momenta at the first subleading order in string coupling, as well as the
effects of a D-/anti-D-instanton pair at leading nontrivial order in the
momentum expansion. These results confirm a number of predictions of S-duality,
and unveil some previously unknown pieces of type IIB string amplitudes.
  Our computation is based on the Neveu-Schwarz-Ramond formalism with picture
changing operators and vertical integration. The naive on-shell prescription
for D-instanton mediated amplitudes, based on integration over the moduli space
of worldsheet geometries as well as the moduli space of D-instanton boundary
conditions, suffers from potential open string divergences and regularization
ambiguities that are in principle resolved in the framework of open+closed
superstring field theory. In this paper, the "on-shell ambiguities" of
one-D-instanton MRV amplitudes are resolved by arguments involving
supersymmetry and soft limits, part of which is verified by a string field
theoretic computation in a highly nontrivial manner.
