Using technology we have today might be enough.
We have ICBMs (InterContinental Ballistic Missile) that could be reprogrammed to become AS (Anti-Spacecraft) missiles. We also have conventional (non-nuclear) explosives that are more powerful than some atomic bombs. If you have fast enough missiles that can out maneuver defensive fire, this could be an effective method of attack. Launching more missiles than the attackers can track and defend against, overwhelming their systems would be another valid attack.
Nuclear missiles could also be useful, even if they don't make a direct hit. These explosions put off a massive EMP (ElectroMagnetic Pulse) that can fry systems within spacecraft. Sure, these spacecraft are designed to handle radiation from space and even fairly nearby suns, but a nuke going off just a couple of meters/yards off their hull is going to be many magnitudes more radiation and EM than that shielding can handle. Space doesn't have the medium for most shockwaves, but an explosion this big will create one for itself. This will likely tear through the hull and any shielding, so any subsequent detonations of nukes won't be shielded against, even if it isn't as close.
The problem with nukes is that at a high altitude, the EMP from the detonation could affect extremely large areas of the ground, too. I don't remember where I read it, but a single nuke detonated at the correct height and location above the USA could knock out the whole country's electronics, unless they were hardened, which most aren't. All consumer electronics, including vehicles, would be toast. Many commercial electronics (including electronics controlling manufacturing, hospitals, airports, and other industry sectors) would also be toast. The military would likely be fine, though.
We have a variety of aircraft even today that can fly so high, it's basically in space. These can be used as launch platforms to get missiles closer to the targets while maintaining good defensive maneuvering. This has the added benefit of surprise, for the first attack, anyway. Most weapons officers would likely realize the atmospheric nature of the aircraft, so write off their attacks as ineffectual. This is why it would only realistically work once, since the weapons officers, or their higher ranks, won't let that mistake happen a 2nd time.
Anything we have currently will only be made better in the future, as well as with alien enhancements to our tech and explosives. If the ground and air forces also have laser, plasma, or rail guns, these can be used as well, if nothing besides keeping the spacecraft busy while the missiles sneak up on them.
Since you have spacecraft to defend, then you can "dead launch" the missiles. This is where you launch them without activating the propellants until they are too close to be defended against. This is tricky, since you are shooting a "dumb" round at a moving target. If you can keep that target in the general area, such as by hemming them in with the ground based attacks, then you can activate the targeting and rockets on the missiles for a now short range attach.
Again, this may only work once. Any subsequent attack like this will be defended against. There may still be times when it works, but only as another "standard" attack with limited results, instead of something decisive.
A "dead launch" from a distance keeps your own craft safe from direct conflict with the attackers. This would help prevent your own attrition while hurting them. Once their weapons, defense, and propulsion systems take enough beating, you can unleash your undamaged ships and take significantly less damage than they inflict. These spacecraft can also be used to ferry/relocate supplies, materials, people, eggs, or whatever around the planet, so they are a critical part of your defense and shouldn't be used recklessly for an attack until it's reasonable the attack will be 100% effective to remove the threat from the planet.
Along with missiles, you can also dead launch magnetic mines that get attracted to the enemy hulls. These can either be detonated individually or they can be programmed to accumulate until there's enough in a specified area to do significant damage. A swarm of "tiny" mines is tougher to target and destroy than a single missile of the same explosive power. This is where the lack of a concussion in space helps, instead of hinders, you. Sure, there will still be fragments that could potentially cause a cascade effect, unless the mines are specifically designed/armored against it. These mines can also be made as shaped charges, so the armoring against fragments would double as the liner. The mines advance armor side toward the enemy, then affix armor side away from the hull. It's not completely foolproof, but would go a long way to making it difficult to defend against this type of attack.
Since the attackers have to carefully pick and choose their targets, you have the advantage. You can blow them up and not have to worry about much. Yes, some of the wreckage will head towards the planet, but significant portions won't. At least not right away. And significant portions of the debris will burn up as it descends, break up into small sections, and even slow down as it becomes smaller and hits more atmosphere. Large sections can be continually hammered with missiles and other weapons until it's small enough to not be a major problem. Yes, large amounts of damage will still happen, but there's only so much you can do to prevent it. If you don't completely destroy the attacking forces, they may decide to try attacking again. Hit them hard and fast enough and they should decide it's simply not worth it.
As other's have mentioned, diplomacy can possibly prevent attacks. Convince the attackers that an area is too important to them to risk a direct attack and they simply won't attack that area, unless it's being used as a military base or weapons supply depot.
Keeping communication open during the battles can also help. Once a section is badly damaged enough, they can offer to surrender themselves. This could be a ground base or a spaceship. Sometimes (maybe most times) it might be more important to save lives as POWs than to kill everyone.
Simply talking your way out of the war completely might not make for such a great book, though. But talking your way out of complete disaster can be useful to end a war before it becomes genocide.
And of course, having orbital systems in place before the attackers even arrives is good. Having satellites that fire missiles, lasers, and all the rest can be the first line of defense. Even using a communications satellite to jam transmissions between spacecraft could be critical during a battle.