 reduces the energy of the impact by 64 times.  Everything on Earth is still dead.
So this is your idea of a "normal" difficulty level?
Present day, so we can't use anything we don't already have.
Thirty days, so we can't develop anything new.
9 billion-billion tons of rock flying at us at Mach 31.
only 18 million miles away, so the only thing between it and us is our moon.
Dude! We're world-builders, not miracle workers.
Fortunately, although you ruled out most of our favorite tools (pseudo-science, playing fast-and-loose with the physical laws, and planet-scale evacuations), you overlooked one of my personal favorites... alternative history.
Let me let you in on a few state secrets. Given that the world is about to end, there is no reason to keep up the charade. Most of the history which you were taught in school was actually an elaborate lie. The cold war, the space race and the star wars missle defense programs, those were all just cover stories, created to hide the most ambicious undertaking in human history. Welcome to Project Star Shield.
For the last fifty years, the Unified Governments of Earth, the covert shadow empire which rules every occupied acre om our planet, has been funnelling a large percentage of our gross planetary profit into preparing for something like Horus. We have amassed thousands of high mass projectiles in lunar orbit. Each projectile masses only a couple of tons, but each is equipped with frozen carbon dioxide tanks which can be vented to sublimate in controlled bursts, impelling and steering these objects through intricate patterns. Recent advances in these trajectory control systems have elevated these projectiles' mobility to the level of surgical instruments.
So here is the plan. We don't have nearly enough projectiles to destroy or even deflect Horos; but we are able to slow it down just a little, enough to change exactly when that massive rock passes across our moon's orbital path. We've done the math repeatedly, and we are now certain that we can arrange a collision between Horus and our moon. With luck, the point of contact will be such that both bodies will be deflected from their current paths, falling into parrallel, sunward-plummeting trajectories. We will loose our moon but we might just save our lives...
This answer is a gutsy one. It doesn't actually answer the original question. The original question asked for realistic solutions to an extinction event asteroid impact on a timeline. However, there is a problem. There are entire teams of Astrophysics PhDs paid to do nothing but solve a simpler version of this problem where all of the design and construction can be done before the asteroid is detected (as opposed to this question, which needs to lump design and implementation into the same timeline) Their answer: we don't really know how to do it. You are not going to get any better scientifically feasible answer than the officially accepted answer in the scientific community that "you simply can't do it."
The v2 Horus is still a ridiculously formidable foe with no real win scenario. However, I think it is getting close enough to being a Kobayashi Maru scenario: no win case, but we might be able to cheat a bit to create a win case.
Using similar logic as in my previous answer for the v1 Horus, we can find that we need to apply a delta-V of.1m/s to the asteroid to deflect it enough to miss earth if we magically had the correct apparatus in place right at the 2 year mark (no surprise, that's 24x less than the velocity needed to deflect the asteroid in the original 1 month timeframe). Unfortunately, even with the decreased mass, we're still looking at $6.55\cdot10^{15} \text{J}$, which is the total energy output of about a million Saturn-V rockets. Realistically, since you'll have to build the craft and send it out, there wont be a full 2 years for deflection, so that number is a gross underestimate.
However, your new numbers got me thinking: 2 years is a long time. Its a time period that allows us to draw on other players besides our self. The general case is "Earth goes squish," but there's no particular reason we have to look at the general case. What if we could come up with a specific case where the geometry lends itself to something more hospitable?
Gravitational slingshots are a well understood force-multiplication tool. In short, a vessel steers near a planet so that its gravity well accelerates the vessel. The vessel can effectively rob some momentum from the planet or planetoid to impart an acceleration or change in direction.
What if, in the specific Horus situation, Horus wasn't actually heading straight towards us, but was actually on a trajectory that bent around a planet to hit us. If so, we might be able to tweak its trajectory to hit that slingshot slightly different. This would be a very effective force multiplication: a small change in entrance velocity into the slingshot would result in a marked difference in trajectory. Why burn a million Saturn V rockets, when you can just use the raw energy of an orbiting planet!
There is a catch: at the speeds Horus is moving, it is only.42AU away from earth when detected. (Poor show, NFO -- missing a small object at larger distances is reasonable, but this is a beast!) Mars has an orbit of 1.55AU, which means even the best case scenario wont let us use any of the outer planets. The closest mars will get to us is still.55 AU away. However, Venus has an orbit of.72AU, which means if the planets align in our favor, Venus could be between us and Horus.
So its time to hack the Kobayashi Maru scenario: when nobody is looking, change any of the randomization features to happen to cause us to detect the asteroid hurtling towards us from the inner solar system. Maybe play it off as though the unspecified ET's that may have sent the asteroid at us wanted to use the effects of the sun to hide the asteroid from NFO, explaining their poor response time. Now, when nobody is looking, change the stardate -- *ahem* I mean Julian date of the scenario to occur when Venus is along the path of Horus, and its gravity well bends Horus into its final lethal trajectory.
This is a small-perturbation model for how much the final velocity changes with respect to changes in the initial velocity. This is our force multiplier term. If it equals 10, it means that a.01m/s change in initial velocity comes out to a.1m/s change in velocity as it hurtles towards earth. The higher this number is, the less effort it will take us to move Horus; Venus will do the rest of the work.
Thus our force multiplier is dependent on the incidence angle. A plot shows this varies from 1.0 at a 0deg angle (perfectly glancing) to 1.34 at a 90deg angle.
This means even with the gravity slingshot, we don't quite get enough oomph to be a useful force multiplier.
But now let's really cheat. This is Kobayashi Maru after all. What if you don't think anybody is looking at the velocity of Venus. After all, they didn't plan for it to be part of the test. What could we do to sneak a solution in to maximize our force multiplier?
where $\mu$ is a ratio between the velocity of Horus and our hacked mass of Venus. A large $\mu$ yields better multipliers, implying Venus is moving at a substantial rate. Venus naturally moves at a rate of roughly.00011 times the speed of light. Venus is supposed to move roughly 3x faster than Horus, so I think they'd notice if we made Venus move at relatavistic speeds, but we should be able to make Venus move 100x faster without anyone noticing. Now $\mu$ is 350, for a multiplier of 150.
A force multiplier of 150 means we now only need $4.3\cdot10^{13}J$, which is only about 750 Saturn-V rockets. This is also on the order of the amount of energy in Little Boy, implying that this multiplier has now brought the problem into the realm of a brute force solution. Kirk will love it.
As long as nobody is checking Venus's velocity, we'll get away with it too.
So a frantic build program by every nuclear capable nation on Earth could launch a fleet of these missiles at the incoming body, with each missile impacting with a Gigaton of energy. Assuming this is a relatively solid body and every missile was programmed to hit at the same slightly off axis point, there could be enough energy transfer to deflect the main body, although Earth would still be hit with a spectacular meteor swarm.
The main issue is that cranking out nuclear warheads on an assembly line basis is not going to be easy or cheap, and for the most part the existing stock of nuclear weapons isn't suitable for making pulse units for the missiles. As well, given the time limits, it would be very difficult to mine, refine and enrich enough uranium (or produce enough plutonium) to make all the pulse units needed; existing stockpiles would have to be used, and existing nuclear weapons stripped down to access their fission cores for material.
Political factors will also be in play; would you hand over your stock of plutonium or highly enriched uranium to the United States to build all the pulse units? Would you willingly disarm yourself by surrendering all your current stock of nuclear weapons to be repurposed into pulse units? For that matter, if the Americans (