  Let $S$ be the 2-sphere and $V \subset S$ be a finite set of at least three
points. We show that for each function $\kappa: V \rightarrow (0, 2\pi)$
satisfying elementary necessary conditions, in each discrete conformal class of
spherical cone-metrics there exists a unique metric realizing $\kappa$ as its
discrete curvature. This can be seen as a discrete version of a result of Luo
and Tian.
