We present data-parallel approaches to solve radial-basis function interpolation problems in the context of partitioned multi-physics simulations, where interpolation methods are required to transfer coupling data between non-matching vertex clouds. Data-parallel approaches are a key component for the efficient use of accelerator cards and thus for performance portability on modern compute platforms. The presented approach is integrated into the open-source coupling library preCICE. After discussing different implementation strategies, we introduce a solution based on the linear algebra library Ginkgo, which provides a common abstraction layer for cross-platform performance with focus on solving sparse linear systems. The new implementation exploits accelerator cards for both, matrix assembly as well as solving the resulting linear system. The capability of the presented approach is compared to already existing implementations in preCICE using a turbine blade geometry.