At least at the moment, I'm not going to bother to write a lot of setting exposition, so we'll start roughly in what would be Chapter 2 of a normal Eden RPG book.  Here, we'll take a brief run-through of attributes, skills, and existing Qualities and Drawbacks.  New Qualities and Drawbacks will be in part 3.  (Yes, Virginia, there is a Gargoyles Quality.  There's probably a Santa Claus, too, but we'll talk about him under the Fey later on.)
 
Attributes - nothing much needs to change about Attributes.
 
Skills - the standard Cinematic Unisystem skill list works just fine for the Gargoyles world.  Occultism clues you in on the secret history of the world, and lets you know about magic and the faeries.
 
Qualities - ah yes, here's the meat of the thing.
 
Attractiveness - The current system, elegant in its simplicity, lumps all matters of personal appearance into the Attractiveness Quality.  So a Gargoyle might start off with -3 Attractiveness to represent his inhuman appearance, but could then buy it up as far as he wanted.  Goliath, who's got a way with the ladies, might have spent 5 points or so to get an effective Attractiveness of 2.
 
I don't really like that.  It's okay in Buffy or Angel, where most of the characters are human, but in a Gargoyles game, it's very possible that all the PCs will be Gargoyles, so it's a little wonky.  I'm seriously considering splitting Attractiveness into two Qualities/Drawbacks.  One would measure your aesthetic Attractiveness, and the other would measure your deviation from human norms.  "Fearsomeness" would be a Drawback that makes your basic form scary/ugly to humans.  It'd give you a negative modifier to Influence tests not based on fear, no matter how high your Attractiveness is - except for dealing with people who are used to your unusual form in some way.  For them, your Attractiveness kicks in.  Possibly rather than all or nothing, the two add/subtract from one another, so a Gargoyle with -3 Fearsomeness and +1 Attractiveness is only two points scary on first impressions.
 
When I get to the point of writing up characters, I'll decide whether to adopt this or not, but I think it makes a neat alternate rule.
 
Enchanted/Superscience item - The relatively high tech level of the Gargoyles setting means that 1-2 point items are frequently not worth paying for with Quality points.  They can just be purchased with sufficient wealth or obtained through Organizations.  Higher-level items should still be bought for 2 points per PL.
 
Optionally, something that would be incredibly expensive like a battlesuit (Which is really several PL 4-ish items all mushed together) can be purchased as a Supernatural package Quality.  The Dual Form Drawback is appropriate to represent the fact that you can't walk around in your battlesuit all the time.

As I've mentioned, I think there's an Eden-approved method for this in All Tomorrow's Zombies.  It involves buying the Robot Quality and whatever add-ons you'd like.  That seems workable to me.  
 
Enchanting/Superscience - Enchanting is completely gone.  Mortal magicians can create potions and charms through a variety of spells, through the Sorcery quality.  More powerful items are purely the purview of the Third Race.
 
Superscience is easier than it is in Buffy.  Superscience devices no longer require special ingredients.  Money works.  This will be discussed more completely later on.  Your Superscience Quality can never be a higher level than your Science skill, and you should probably really have Science of at least 4 before you pick up Superscience.  6 would be better.  We're probably going to talk about new uses of Superscience to cover metagenetics and cybernetics.
 
Occult Library - I think Occult Library works just fine as-is.
 
Rank - Rank now explicitly buys up your standing in an Organization, granting you more autonomy (but also more responsibility).  We'll talk more about Organizations when I get into new Qualities/Drawbacks.  You can have Rank in several groups.  For instance, an undercover police investigator might have rank in the Police and in an organized crime ring.  Almost all Illuminati members also have Rank in some other group.  In fact, that's frequently why they were recruited into the Illuminati.
 
Robot - The Robot Quality from Buffy is a decent starting point for any robotic characters, but there's no reason to limit yourself so.  Instead, build Robots like Demons and Supernatural characters from Angel.  Robots can have Drawbacks like Beholden from Armageddon (which I might list down in the next part, for simplicity sake).  They could also have variations of Antisocial Tendencies, Mental Problems, Emotional Problems and the like to represent programming imperatives.
 
Cyborgs work pretty much the same way, except they can recover (depending on how many cybernetic parts they have) 75%, 50%, or 25% of their Life Points without a Mr. Fix-it test.  Cyborgs who are nothing but a brain in a robot body work just like normal robots.  Drawbacks like Cruel are appropriate to represent the dehumanizing effect of losing so much of your essential humanity.  (Then again, Jackal and Hyena were already pretty twisted)
 
Sorcery - Sorcery works as-is, except that I'd drop it to 3-points per level and remove the TK.  Pretty much only Faeries have Sorcery, and some of them might instead have 2-point per level Magic Domains, which are pretty much Invocations as per the conversion rules in the Magic Box.
 
Vampire - no Vampires have shown up in Gargoyles, thus far.  If they do, the existing Vampire Quality probably won't really work for them, but do whatever you want with your own game.
 
Wealth - Wealth, at high levels, gives you free levels of the Organization Quality.  At level 4, you get 5 Organization points.  At level 5, you get 10.  Beyond level 5, Wealth would start to describe the resources of nations.  Characters might actually be that rich (like David Xanatos), but level 5 represents the limit of their liquid assets, so this Quality is capped at 5.  (To keep the Director sane, really)
 
Supernatural Qualities - Note that many Supernatural Qualities are appropriate for Demifey, Mutates, and Cyborgs.
 
Natural Attack - New to this Quality is an Armor-Piercing kicker for 2 points.  It'll probably work with Supernatural Attack, too, but I'd be more hesitant to apply it.
 
Supernatural Senses - New to this Quality is night-vision, costing 1 point.
 
Okay, so I think that does it for existing Qualities.  Next up are the new ones.
 
Magical Conduit (2-point per level Quality)
A Magical Conduit is a mystical artifact that allows a human to freely work magic.  Each level of Focus allows a non-Sorcerer to Quick-Cast spells of a power level up to the level of the Quality.  A would-be magician can only control a Conduit of a strength equal to or less than his Occultism level.  Otherwise, his spells have the chance to go seriously awry - using the miscast rules in Buffy.  A Magical Conduit is essentially an enchanted item, and can be lost.  
 
Magery (1-point per level Quality)
Magery provides bonus points on Sorcery checks.  The maximum rating of this Quality is 5 levels.
 
Organization (Variable Quality)
The Organization Quality provides a character (or characters, it is possible to pool levels) additional Organization points.
 
Supernatural Qualities - Supernatural Qualities are possessed by such creatures as Gargoyles, Demifey, Mutates, and Cyborgs.  To create such a character, you build a package Quality by picking the positive and negative traits you want to be intrinsic to your character's "race."  (In the case of a cyborg or mutate, it might be a race consisting of a single creature, of course.  Each demifey might be unique, as well)
 
Extra Limb - Variable Quality
You have one or more extra prehensile limbs.  Extra feet don't really cost you anything.  This Quality doesn't grant you any additional actions, but it can allow your actions to affect more people.  If you had, say, ten tentacles, you might be able to grab ten people a few at a time and hold/crush them all.
 
One limb costs you 1 point.  2 to 4 additional limbs cost 2 points.  5 or more cost 5 points.  In practical terms, 10 limbs is probably a good limit to this Quality.  Extensible limbs that significantly increase your reach add a 1-point kicker if you can reach about 10 feet (3 meters or so), and 2 points if you want to be able to reach even further.  And at some point you're just getting silly.  Particularly at the higher levels, your limbs don't have to be static limbs.  An amorphous mass that can extend multiple tendrils might vary from no limbs up to ten, depending on his mood.
 
Magical Affinity (2-point per level Quality)
Each level of Magical Affinity gives you a +1 bonus on Sorcery tests, up to a maximum of 5.  Unlike Buffy Sorcery, there is no progressive spell-casting penalty, so there is no point in taking this Quality beyond 5 levels.  The prerequisite for this Quality is Sorcery.
 
Special Movement (Variable Quality)
This Quality imparts more freedom of movement.  Characters can have more than one type.  For instance, Gargoyles have the first level of Climbing, and Gliding, for 3 total points and pretty much as much freedom of movement as someone who can just fly.
Climbing: 1 point for climbing with claws/special gear.  2 points for spider-like wall-crawling that lets you hang from the ceilings as well as scaling the walls and climb smooth surfaces easily.
Flight 3: points for flight that can be easily disrupted (like with wings), 5 points for freeier flight.
Gliding/swinging: 2 points.  It's pretty much just the lower level of Flight.
Leaping: the ability to make prodigious vertical or horizontal leaps.  2 points.
 
Superspeed (2-point per level Quality)
Superspeed lets a character move really quickly.  It's generally tied to a single type of movement, like running, swimming, or flying, depending on the character.  Each level of Superspeed more or less doubles the character's maximum speed.  At level 3, the character can move as fast as a car in the city.  At 4, he's approaching race-car speeds, and at 5, he's... well, really fast.  Superspeed doesn't allow any extra attacks.  For that, you're going to want obnoxiously high Dexterity.

I think that covers new Qualities.  I was planning to do Packages as part of this post, but it's getting late tonight and I still have some work to do on them.  I'll do them next.  Really, you don't HAVE to have package qualities to start using this stuff, so I don't feel too bad about leaving you waiting.