This has been a touchy subject with many concerned about the balancing of these mobs but I believe I have a very good idea to consider. I have checked the forums and didn't find any similar posts so my apologies if I missed something. The main point is to implement these creatures using the already established invasion system, with the details to be hashed out below.
Edit: I have seen the Ered Mithrin thread (http://lotrminecraftmod.wikia.com/wiki/Thread:256082) and I am giving credit to ZombieLizard for his ideas concerning dragon health, size, and item drops. My suggestion deviates in reference to details on implementation and attacks.
Dragons: These creatures are rare but extremely powerful. They should have between 150 (ZombieLizard) health and have several modes of attack: an aerial fireball and firestream attack, and tail swipe, claw, and bite attack when on the ground. the fireball attack should do 3 hearts of damage (unarmored) with perhaps some knockback and fire damage as well. firestream might do about 2 hearts with fire damage. tail swipe should do 4 hearts of damage (unarmored) and knockback. Claw attack should do 5-6 hearts (unarmored) and the bite attack might do 7-8 hearts or possibly more, due to the fact that if you're in the dragon's jaws then you're probably screwed anyway. Now, dragon invasions should be universally hostile and should be given a higher degree of rarity than just "rare" in all biomes north of Harondor except the Grey Mountains which will be "rare," and the withered heath with an "uncommon" rating. Biomes south of Harondor shouldn't experience dragon invasions. Concerning drops and a corresponding achievement look at ZombieLizard's thread (link above). Each invasion should only include 1 dragon as they are solitary creatures.
Eagles: Eagles will be "good" aligned invasions, spawning in all biomes while sharing the "more than rare" rating of the dragon invasions. Each Invasion might include 3-6 Eagles. Eagles would use ground based "claw" and "bite" attacks similar to but doing less damage than a dragon's. Eagles would also have an aerial attack that might do just 4-5 hearts of damage, or less damage and knockback. Eagles would have 80-100 health and drop eagle feathers, bones (perhaps a head for decoration?) and something else, ideas welcome.
Fell Beasts: counterpart to the Eagles, with similar mechanics but for "evil" factions. drops include claws, bones, and maybe a head.
OPTIONAL: many players relish the idea of using fell beasts and eagles for mounts but in order to keep these balanced, i propose making them outrageously hard to acquire. Eagles and Fell Beasts might have their own alignment bars and will be cumulative of all good/ evil alignment. the trick is that 10-15 thousand alignment is required to approach the lord of Eagles (or fell beasts) and once accomplished a not-so-mini quest must be completed before a player can hire one eagle/fell beast for an exhorbitant amount of money. players can only posess one eagle/fell beast.
This concludes my suggestion, while I'm sure this might cause some controversy I welcome positive criticism and any ideas that will make this suggestion better. thanks.