is there anything stopping the Good-aligned 'Necromancer'?
There shouldn’t really be one anyway.
Is there anything stopping you using Animate Objects, with or without Permanency, to affect a bunch of corpses? If so, what? And would that qualify as an Evil, Chaotic, or Neutral act?
I believe corpses are objects, on the basis of the definition of an object (something without a Charisma or Wisdom score) and what it means to have or not have those abilities:
Any creature that can perceive its environment in any fashion has at least 1 point of Wisdom.
Any creature capable of telling the difference between itself and things that are not itself has at least 1 point of Charisma.
Since a corpse is neither self-aware, nor aware of its surroundings, it should not have Charisma or Wisdom scores, and therefore should be an object.
Moreover, a creature (that is, a not-object, since in game terms everything is either a creature or an object), requires being “alive or otherwise active,” which a corpse isn’t generally.
That said, the game never comes out and says that corpses are objects, and several spells that specifically target corpses lack the (Object) notation that they should have (including some that allow saving throws). Finally, a lot of object-targeting spells were most likely not written with corpses in mind. The mending spell, in particular, seems problematic (since it means a cantrip can do what a higher-level spell, gentle repose, does, and that’s not supposed to happen).
Anyway, point is, if a corpse is an object (and I think it is), animate objects seems (oddly enough) legit. The animate objects spell isn’t inherently Evil like animate dead, nor will your animated corpse involve a soul forcibly bound to it or whatever it is that makes animate dead evil in the first place. Depending on your setting, desecrating a corpse may be considered Evil or un-Lawful.
Have you ever heard of this being done?
No, I have not.
It Depends on the Cleric's Deity
The cleric's class features include the class feature titled Chaotic, Evil, Good, and Lawful Spells, which says
A cleric can’t cast spells of an alignment opposed to his own or his deity’s (if he has one). For example, a good cleric (or a neutral cleric of a good deity) cannot cast evil spells. Spells associated with particular alignments are indicated by the chaos, evil, good, and law descriptors in their spell descriptions. (PH 33)
Emphasis mine. Thus a neutral cleric of an evil deity could not cast spells with the good descriptor, and that includes most sanctified spells. A neutral cleric of a neutral deity could cast sanctified spells (but might be reluctant to do so or might follow that by casting corrupt spells to preserve the balance), as could a good cleric of a good or neutral deity.
As KRyan's Comment pointed out, "A cleric may not be neutral unless his deity's alignment is neutral" (PH 31), so there's just no such thing as a neutral cleric of a good or evil deity.
The Eberron Exception
It bears mentioning that the Eberron Campaign Setting text loosens the above restrictions as follows:
A cleric can cast spells with any alignment descriptor. Casting an evil spell is an evil act, and a good cleric’s alignment may begin to change if she repeatedly casts such spells, but the deities of Eberron do not prevent their clerics from casting spells opposed to their alignments. This rule supersedes the information in Chaotic, Evil, Good, and Lawful Spells on page 33 of the Player’s Handbook. (ECS 35)
Sanctified spells, however, remain exclusive to good and neutral clerics of good and neutral deities: "Evil characters cannot cast sanctified spells, including ones cast from magic items" (BE 83).
Best Answer
1) If the Cleric is a PC his alignment is his choice and can change suddenly at any time. As long as his God is okay with it, he can suddenly turn evil, cast the spell, then turn good again according to the RAW in the atonement spell description.
2) If that's not allowed he can use the Atonement spell, but since he's deliberately casting an evil spell, he will have to pay the 500 XP penalty cost. This is pretty reasonable as a get-around-a-class-restriction fee.
3) The Cleric can hire a buddy, preferably another Cleric of the same God, who's less undercover about being evil. This costs ~87.5 gp, but you can probably get it for less if you just time-share with a necromancer-Cleric who was gonna be doing it anyways. The latter case assumes you don't need this done on a specific area.
4) Summoning's no good here, since none of the summons available at Summon Monster V or below have access to the spell. You CAN use Lesser Planar Ally to summon a Neutral or Evil Aligned level 3 Cleric of your God who currently has Desecrate prepared, but this'll end up costing you 100gp and 100XP, plus the cost listed in number 2, so it's not a good idea unless there's no similarly-aligned evil Clerics around for hire.
5) You could find a Nightshade and try to sneak up close to it or manipulate it into going where you need it or make a deal with it, but this'll probably just end with you (un)dead. Unless you are already, in which case this is probably legit. You can do this with creatures merely capable of casting desecrate (perhaps at will), but then we're clearly back to number 2.
6) You could try doing it the old fashioned way, where you brutally murder a hundred innocent (preferably high Cha virgins) villagers and scrawl in their poo and blood prayers to your demonic masters and insults to everyone in general upon the target of your desecrate, while burning long candles of their fat embedded in the piles of their skulls in a pentagram around the thing you want desecrated (and then see if your GM lets this emulate a desecrate spell). Make sure you cast lots of summon monster [good] spells and force the celestial beings to join you in your murderous ritual, so that you keep your alignment up. This is only recommended if your real alignment is Lawful Evil (If your response is "What do you mean, 'real' alignment, I'm as good as the rest of you", this is you).
7) Limited Wish and a lot of other spell duplicating magic can do this, but no spell-duplicating spell capable of doing this is less than 7th level (Shadow Evocation, notably, only duplicates Sorcerer/Wizard spells).