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Synchrotrons produce continuous trains of closely spaced X-ray pulses. Application of such sources to the study of atomic-scale motion requires efficient modulation of these beams on timescales ranging from nanoseconds to femtoseconds. However, ultrafast X-ray modulators are not generally available. Here we report efficient subnanosecond coherent switching of synchrotron beams by using acoustic pulses in a crystal to modulate the anomalous low-loss transmission of X-ray pulses. The acoustic excitation transfers energy between two X-ray beams in a time shorter than the synchrotron pulse width of about 100 ps. Gigahertz modulation of the diffracted X-rays is also observed. We report different geometric arrangements, such as a switch based on the collision of two counter-propagating acoustic pulses: this doubles the X-ray modulation frequency, and also provides a means of observing a localized transient strain inside an opaque material. We expect that these techniques could be scaled to produce subpicosecond pulses, through laser-generated coherent optical phonon modulation of X-ray diffraction in crystals. Such ultrafast capabilities have been demonstrated thus far only in laser-generated X-ray sources, or through the use of X-ray streak cameras.