I'm looking for an adjective that describes a living being as having very long ears (rabbit, donkey, etc.) preferably ending in "-uous".
I believe you're looking for macrotous.
You should probably just go with "long-eared" — I don't think there are any specific terms meaning that, except possibly scientific ones with Latin roots.
Huh, you might say the animals have pendulous ears. That emphasizes the weight of the ears, as well as suggesting they hang in a droopy fashion.
Hyperotic could be construed to mean "over-eared" (otic), though the folks at Urban Dictionary have other ideas about the definition.
There's always "asinine". Although that does imply dim-witted, as well as visually reminiscent of a donkey, which is maybe more of an implication than you wanted!
How about Vulpine - of or relating to a fox. "He had vulpine ears"