We investigate the noise properties of pump currents through molecular wires and coupled quantum dots. As a model we employ a two-level system that is connected to electron reservoirs and is non-adiabatically driven. Concerning the electron-electron interaction, we focus on two limits: non-interacting electrons and strong Coulomb repulsion. While the former case is treated within a Floquet scattering formalism, we derive for the latter case a master equation formalism for the computation of the current and the zero-frequency noise. For a pump operated close to internal resonances, the differences between the non-interacting and the strongly interacting limit turn out to be surprisingly small.