The K-theoretic Schubert structure constants of a homogeneous space G/P are known to have signs that alternate with codimension by a result of Brion. For Grassmannians of type A, these constants are computed by a generalization of the classical Littlewood-Richardson rule that counts set-valued tableaux. The K-theory ring of any Grassmann variety is generated by special Schubert classes that correspond to partitions with a single row. I will present positive combinatorial formulas for the structure constants in products involving special Schubert classes on any cominuscule Grassmannian. For maximal orthogonal Grassmannians this confirms the Pieri case of a conjecture of Thomas and Yong. This is joint work with Vijay Ravikumar.