You could do it with 1960s computers and whatever Sci-fi Magic propulsion system your probe needs to get from system to system. Find a big asteroid. Accelerate it into the orbit of the planet at, oh, .01c should be plenty. What is the planet going to do, roll a natural twenty to dodge?
In _The Killing Star_ advance probes locate almost every settlement in the Solar System and every one is hit with relativistic projectiles. Earth itself is blanketed with an entire grid of such impactors -- from opposite directions, so the whole surface is bombarded. 99.9% of humanity dies in the space of several hours.
Since the projectiles are relativistic, there is no warning.
There's no conventional or nuclear way to generate enough directed energy to push a decently sized asteroid, on a straight course for the planet and within a reasonable distance of it, away.
An asteroid with a diameter of 2 km and a density of 1 ton/m^3 weighs ~410^9 kg. Travelling at 0.01c, it has a kinetic energy of ~410^22 J, or ~100 times the current worldwide energy production per year.
Of course deflecting it doesn't require you to fully stop it, but it's closing in fast and you need a strong sideways push to accelerate it fast enough to end up with enough speed to miss the planet. If we ever see an reasonably sized asteroid with reasonable speed on a collision course, we're as doomed as if we hadn't seen it.
Actually there is - like most technology it all scales up, and if it happens you bet we'd all be in factories churning out nukes/rockets if we had to. If you do the numbers, sure it comes out big, but 4 billion kg is not really that much - especially compared to the production capacity of 6 billion people over a couple of days. We could produce the required energy to move it by collectively winding handles let alone manufacturing nukes.
Besides that impending death is an excellent motivator.
If the projectiles are relativistic, then warning could only be a few days or even a few hours ahead of time. Even relativistic impactors are unnecessary. Low albedo impactors coming in from angles far off the ecliptic would be exceedingly hard to spot.
You could do it with 1960s computers and whatever Sci-fi Magic propulsion system your probe needs to get from system to system. Find a big asteroid. Accelerate it into the orbit of the planet at, oh, .01c should be plenty. What is the planet going to do, roll a natural twenty to dodge?