So, the rules here are a bit of a mess.
First, we have the description in charnel touch that describes the negative energy concentrating in the dread necromancer’s hands—but that’s just fluff. Descriptive statements like this are sprinkled throughout 3.5e, and are consistently only meant as just that, description—not proscriptive rules requirements. This has come up a few times here, if you want to see some other examples—there are many more. So that should be ignored.
Second, we have the question of how supernatural touch attacks are delivered. The rules for touch attacks are in the section all about spells, specifically, and the rules for “touch spells in combat.” They don’t mention non-spell touch attacks much at all. So the question is, do these rules apply to supernatural touch attacks—and if not, what rules do apply to them? Simply for sheer lack of any other rules to fall back on, I would argue that these rules must apply to non-spell touch attacks.
Relevantly, one of those rules mentions natural weapons:
Holding the Charge
If you don’t discharge the spell in the round when you cast the spell, you can hold the discharge of the spell (hold the charge) indefinitely. [...] Alternatively, you may make a normal unarmed attack (or an attack with a natural weapon) while holding a charge. [...] If the attack hits, you deal normal damage for your unarmed attack or natural weapon and the spell discharges. If the attack misses, you are still holding the charge.
So with holding the charge, not only can the darfellan use their bite to deliver charnel touch, they can actually include their bite damage along with it, if they target regular AC instead of touch AC.
Complete Arcane page 73 goes into somewhat more detail on this... except it fails to mention natural attacks, and focuses solely on unarmed strikes (while again focusing solely on touch spells):
Improved Unarmed Strike: You can add the damage of your unarmed strike to the damage of a touch spell by delivering the spell as a regular melee attack instead of a melee touch attack. The defender gets the full benefit of armor and shield, but if the attack hits, the unarmed strike deals normal damage over and above any damage the spell does as it is discharged. If the unarmed strike misses, then the spell is not discharged.
Again, I would argue that this is specific to unarmed strikes for much the same reason I suspect that the touch-attack rules all focus on spells: Player’s Handbook and Complete Arcane are player-focused books. Spells are what player characters, by and large, actually have. At this point in 3.5e’s publication history, the only supernatural touch attacks offered by classes were the paladin’s lay on hands and the blackguard’s deadly touch—not a whole lot. Likewise, barring wild shape or polymorph effects, the only option for natural attacks for players were found level-adjusted creatures in Monster Manual. So I think they just stuck to the most-expected cases (spells, unarmed strikes) for simplicity/word count. I cannot back this suspicion up with any hard evidence, however.
Thirdly, we have a question of how charnel touch interacts with the action economy. The default rule for supernatural abilities is that they take a standard action “unless otherwise specified.” In the charnel touch description, we have “At will, but no more than once per round, she can make a melee touch attack,” which makes absolutely no sense as a restriction if it takes a standard action anyway. There are a very few ways to get a second standard action in a round, but none of them are natively available to a dread necromancer or found in Heroes of Horror. In other words, I have always read this description as specifying that charnel touch, unlike other supernatural abilities, does not use a standard action, but rather can simply be used in place of any attack the dread necromancer would otherwise get to make.
That would include the attack the darfellan could have used to bite.
A darfellan dread necromancer could choose to deliver a charnel touch attack instead of, or along with, his bite attack. If he chooses to deliver it with the bite, it must hit the target’s regular AC, rather than its touch AC, and on a critical hit only the bite damage, not the charnel touch damage, is doubled. If he chooses to deliver it as a touch instead of the bite, then he gets to target touch AC, but misses out on bite damage. (For most dread necromancers, against most targets, the expected damage is higher with the touch attack, because their chance to hit is so much higher and the bite damage itself doesn’t add so much.)
In both cases, any penalties the bite attack takes, for example for being a secondary attack (if the darfellan had also attacked with weapons), would also apply to the touch attack.