Spin vortices in magnetic nanopillars are used as GHz oscillators, with frequency however essentially fixed in fabrication. We demonstrate a model system of a two-vortex nanopillar, in which the resonance frequency can be changed by an order of magnitude, without using high dc magnetic fields. The effect is due to switching between the two stable states of the vortex pair, which we show can be done with low-amplitude fields of sub-ns duration. We detail the relevant vortex-core dynamics and explain how field anharmonicity and phase control can be used to enhance the performance.