How would a big rock even get accelerated to near-c speeds? I have personally never seen or heard of a ship with "fittings" of some sort for holding an asteroid several times its size at near-c speeds and releasing it with aim of some sort.
What fittings do you need, really?
Densitometer to map its mass distribution, your computer should be able to calculate its CG, then burn a depression into one end so that a ship parked there is pointed at the CG.
Then you just accelerate....
How about filling a hollow asteroid with bombs or nuclear material? Then even if the asteroid itself gets destroyed, you still have a lot of bombs or radiation in the atmosphere.
A 1 km rock moving at ~.95c will hit with impact energy on the order of 100,000,000 teratons of TNT. A 500 megaton nuke going off would be a dead spot in the explosion.
If the rock gets destroyed far from the target, the 500 MT bomb harms nothing, since nothing is nearby.
If the rock gets destroyed within a light-second or so of atmosphere, well, you get 100,000,000 teratons spread evenly over the entire hemisphere toward the rock. In which case, the 500 MT is still a deadspot (you're already getting 500 MT of energy deposited on every 6 km^2 of the planet's surface (assuming Earth as the target)....
There really isn't much you can do to make a relativistic rock more deadly. Other than just make it bigger. Nor is there much you can do to wreck one unless you can spot it a LOOOOOOOOONG way out.
Blow it up as it's passing Luna, and it has less than 1.4 seconds to disperse (which means it'll still hit a 100 km diameter circle).
Blow it up out around Mars orbit? That'll probably mean that a little bit of it will miss the planet, but mostly it still hits as what amounts to a honking huge fusion gun blast (call it 50,000,000 teratons equivalent).
Note, for reference, that at 0.95c, to wreck it out beyond Mars, assuming:
1) your fleet can be underway an hour after detection,
2) your fleet can accurately hit an object 1km in diameter moving a near lightspeed,
You'd then have to detect it at 2333 AU (for reference, Pluto is 40 AU out)
Under those conditions, you get ONE shot. After that, your fleet is past it and won't ever be in position to try again.
For every ~20,000 AU farther out you detect it, you get an extra shot, to the limit of the number of ships you have, so if the first ship/group misses, there's another ship/group an hour behind it to try again.
Or only ~7000 AU extra distance if you want 20 minutes (one space combat turn, MT rules) between shots.
Good luck with that....