Transversity generalized parton distributions (GPDs) can be probed in diffractive electro- and photoproduction of two vector mesons on a hadron in kinematics where the two vector mesons are separated by a large rapidity gap. We report on calculations for this process in the case of coherent $\rho^0-\omega$ meson production on a deuteron target. Our cross section results show that an electron-ion collider with deuteron beams and forward detectors could probe deuteron transversity GPDs.