What you're after, is probably not a resonant frequency. Resonance means stress/strain is peak at periodic intervals through the material. Perhaps a plane wave can be applied, at the right frequency, with the right mounting (because boundary conditions matter for reflection and absorption), and perhaps the material is consistent enough (similar density, modulus, speed of sound) that, you can manage to get a line or plane of maximum strain right across a bedding plane, and *pop* off it goes.
But that's a looong list of assumptions, for a material that is explicitly inhomogeneous -- not to mention, once a crack forms, the properties of the material change (as the crack region turns from solid to broken, suddenly it's a lot more flexible), and most likely more power and a lower frequency are needed to continue spreading it.
This sounds more like something that needs piezo stacks to do? The displacement is small, probably tens or hundreds of microns, and the force (static and dynamic) need to be quite large. A magnetic transducer can't really do either one; imagine clamping down on a loudspeaker cone for example. The frequency range is also much higher -- when you hammer a rock, that "tink" sound is its (and the hammer's) resonant frequencies, mostly low order flexural and longitudinal modes. This is largely in the kHz, and the stiffness and density (at least of a solid homogeneous sample) are well matched to piezo transducers (being ceramics themselves).
I don't know how you'd mount it. Fluid, maybe? You'd have to use liquid metal, if you want density comparable to the material. Maybe some mismatch would actually be desirable, to get some system Q in the resonances? Then you could maybe get in-plane resonances of low order and hope to crack it in layers of half, thirds, etc. Solidified metal might work too, as long as it fits tightly; several low-melting alloys expand on cooling, which might serve to clamp it in place, I don't know. Or maybe it needs to be epoxied in place, so there's some holding force. Or perhaps the samples are usually oversized, and can be polished down to flat planes, then clamped between metal anvils and vibrated.
Yeah, as mentioned, clamping or vibration on a concretion will simply crumble from the contact points (or worse) -- but this is still true even of very hard rocks, the contact points are stress raisers and will crumble under sufficient load. We're talking enough load to try and cause internal rupture, and it's a good bet that at least as much force will be required on the rock surface to get there. You need a wide contact area to have any hope of distributing that load.
Tim