In Blood War, Demons kill Devils.
However, many Devils have the regeneration special ability.
Demons never use Good-aligned weapons and spells.
So... how do they kill those?
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Because the wording used across all of 3.5 is the same standard boilerplate for anything that isn't the align weapon spell or the holy weapon property, there is a shocking gulf between the kinds of things one would expect to work, and what actually does. The fact that creatures with an alignment subtype have their natural weapons treated as having that alignment "for the purpose of overcoming damage reduction" means they don't actually have that alignment - and that's the wording you will find on virtually every other method of attuning your weapon to hew through a creature's native defenses.
"For the purpose of" limits it far more than it arguably should, though that gets into a question of RAI. I would personally be extraordinarily surprised if every author who copypasted that rule actually understood how it related, as written, to regeneration, since aligned regeneration is considerably harder to contend with under these terms than any other kind of regeneration. Troll regeneration is a unique tactical question, a signature characteristic, and a mild inconvenience. Conversely, aligned regeneration requires (in this instance almost literally) a silver bullet.
What this leaves us, per RAW, is that a celestial with silver-coated talons can't do anything more to a cornugon than a mortal with a butterknife, not unless good-aligned damaging spells enter the picture, and as we already know, demons don't have ready access to those. Of the methods that are most viable to address regeneration, demons don't generally have 5th level spells on hand to cast graymantle, trollbane works as a poison and so doesn't work on devils, and of course the actual vulnerability in question - good-aligned weapons - is something of a non-starter.
Now, of course, the armies of the Abyss, not unlike the armies of Hell, have assets other than demons - it's quite feasible that a mortal spellcaster with access to graymantle is available to help put down a cornugon, at least from time to time. That being said, spell resistance makes that a horribly unreliable method.
...but then you have the lilitu. A lilitu is capable of using holy weaponry without taking the penalties normally associated with it, and can use other good-aligned items (including scrolls of holy smite etc.) with total ease. Capable of using detect good at will and practiced specifically in the art of deceiving and undermining religious faith, a lilitu likely has access to such materials as needed and would find it hilarious to turn the tools of benevolent gods to the purposes of the Abyss.
Now, that being said, "special forces" isn't really a lilitu's purview, or her field of interest; lilitus do not like to engage in melee combat and probably don't care about the Blood War at all. As demons, and thus paragons of selfishness, they would have very little reason to get involved as cornugon-busters.
That being said, if you are cleaving to hard RAW exclusively, then lilitus paid or coerced into service as blasphemous mockeries of paladins are an absolutely valid way that demons can kill regenerating devils.
These elite devils also had the ability to regenerate in 2nd Edition, and demons had no unique capability to pierce it at that time either. This is relevant because 2E introduced the Blood War and talked about it at length. From Hellbound: The Blood War, we are specifically told:
For example, many fiends who fall in battle regenerate and rise to fight again - unless, of course, they're dispatched for good. Mortals can help make sure a dead fiend stays dead by dousing it with holy water or whacking it with a holy weapon.
So it seems that the favored solution, by and large, is just to beat the absolute stuffing out of anything that can regenerate to the point that it either elects to leave or can be dealt with using a handy mortal underling with a blessed silver dagger.
...that same book also tells us that, since so many of their spell-like abilities are garbage in the Blood War, many fiends of all stripes work to develop different abilities, or seek to master spellcasting - some by trading away their capacity to use spell-like abilities. Such fiends could certainly pick up assets such as the graymantle spell which would at the very least give pause to a normally confident gelugon or cornugon.
There's also the simple fact that in the chaotic realms of the tanar'ri, an endless variety of horrifying types of demon exists within the roil of the Abyss. There's no reason why there wouldn't be one or more breeds ideally suited to breaking through such regeneration - perhaps counterparts to the ghoulish maurezhi and nabassu, which gain power by eating humanoids, there could exist some manner of scavenger fiend herded into Blood War battlefields to seek out unconscious baatezu whose wounds are reknitting and gnaw them to death.
Lastly, of course, we can simply look at it from the Doylist perspective and say that it's one of those omissions in what RAW contains based around the rules that would generally be needed for players and DMs - the relevant ability for demons to handle elite devils does exist, at least at some echelon; it was simply never written into their descriptions as it would not, by and large, be pertinent to the experience of using such monsters in average play. When it comes to planar ecology and interaction, this sort of omission is readily apparent in 3.5 - see for example what happens to undead on the Positive Energy Plane (they just get healthier and healthier forever, as they are never required to make the Fortitude save by RAW).
Regenerating creatures can be killed
The description of the Regeneration power includes:
A regenerating creature that has been rendered unconscious through non-lethal damage can be killed with a coup de grace (see p153 of the Players Handbook). The attack cannot be of a type that automatically converts to nonlethal damage.
Attack forms that don't deal hit point damage (for example, most poisons and distintegration) ignore regeneration. Regeneration also does not restore hit points lost through starvation, thirst or suffocation.
In short, a demon can most commonly kill a devil by reducing it to unconsciousness and administering a coup de grace.
EDIT: As @Mouza noted in comments to this answer, the coup de grace damage must be done with a damage source that is not automatically converted into non lethal damage. For the subset of devils that possess the regeneration ability, this varies. For the chain devil, silvered weapons will suffice, there is no need for the weapon to be good aligned. For others, such as the Horned Devil, the weapon must be either silver and good-aligned or a spell with the "good" descriptor (hence the OP's question). However, while devils are immune to poison, they are not immune to starvation, thirst or suffocation. Starvation and thirst are too time-consuming for most battles (but would likely be preferred by sadistic demons as a means of executing prisoners if feasible), but suffocation is an option which could be implemented on the battlefield. The devil would presumably need to be either restrained once unconscious or continually damaged while suffocation was ongoing to prevent it breaking free.
If the demon has other powers that do non-hit point damage then they can use those also (although devils are immune to poison unless noted otherwise). The battle between a demon and a devil may take a long time given the effects of both regeneration and damage reduction, but neither side has anything better to do.
Not many devils have regeneration which requires good-aligned weapons.
The SRD lists eleven types of devils. Of these, only four have regeneration; of those, kytons (chain devils) have regeneration which can be overcome by silvered weapons (or good). A demon army fighting devils will almost certainly be carrying plenty of silver in order to overcome the DR on all low-level devils, so kytons are a non-issue.
The other three are gelugons (ice devils), cornugons (horned devils), and pit fiends (run away).
Gelugons (CR 13) are typically commanders and strategists, so they will be rare creatures among vast masses of lower-powered troops. A demon army might have a few specialists who are capable of dealing with gelugons - maybe some unlucky demon who has to suck up the penalty for using a captured good-aligned weapon, maybe non-demon creatures who have been compelled or paid to help out - but they don't need a lot of gelugon-killers.
Pit fiends (CR 20) are also commanders, and very rare. For any force to destroy a pit fiend would be an exceptional event.
Cornugons (CR 16) function variously as force commanders or as shock troops. However, their high CR implies that they're pretty rare. An opponent strong enough to be taking on an entire squad of CR-16 monsters at all should have some options for doing lethal damage here.
Outsiders breathe, but do not need to eat or sleep (although they can do so if they wish).
- Monster Manual p. 313 (Outsider Type)
Attack forms that don’t deal hit point damage (for example, most poisons) ignore regeneration. Regeneration also does not restore hit points lost from starvation, thirst, or suffocation.
- Monster Manual p. 314 (Regeneration)
So starting here, we have a clear vulnerability that most fiends possess, even the ones with regeneration: Suffocation. All we need is a way to exploit it.
A wand of create water (the spell being an orison for clerics, such as many middling fiends) is valued at 375 gold pieces, a steal in relation to any spoils that might be won. All that's demanded once the demons have scored their victory in battle is a low point in the earth, or some manner of hole, for holding the water. Even a portable hole could work; the suffocation rules apply as per usual, and water just helps it along.
Some would say that using magic items like this is not the domain of demons. I say demons often have Intelligence scores above 8.
I find I have to disagree with one of the question's premises, namely -
Demons never use Good-aligned weapons and spells.
Why not? While demons will indeed suffer penalties for toting around good-aligned weapons, I can imagine a weapon with the Holy Enchantment on it would be quite valuable to a demon fighting against Devils, or in fact, even other demons. The only penalty for wielding such a weapon is gaining a permanent negative level...this seems to me like a small price to pay for a method of permanently overcoming such common adversaries.
Similarly, what would prevent a Demon or Devil from carrying around and UMDing scrolls of Align Weapon? Or even flasks of Holy Water? (perhaps stored in lead-lined boxes to prevent any possible cross-contamination)