Unlike the Daedra, these don't have an organized each-prince-has-a-quest-and-good-reward
format. But they do exist, although we'll have to define them more loosely:
Kynareth - Weak albeit unique reward. Unless you like saving trees. A lot.
AFAICT the following have no proper quests:
Arkay (aside from a minor fetch quest in Whiterun that nets you a pittance in gold)
Stendarr (But since the Vigilants of Stendarr are out and hunting werewolves, it's entirely possible in DLC. They have a lodge in Dawnstar.)
Talos (well, aside from fighting the Thalmor at every turn)
There are some Daedric quests that might be fine for your paragon of morality to still do. I'll try to avoid spoilers, but here are the Daedric Quests by prince and evilness:
Azura - Just some necromancer hunting
Clavicus Vile - Just don't do everything Clavicus says
Malacath - You ultimately help the Orcs
Meridia - Pretty much the definition of Lawful Good
Nocturnal - Part of the Thieves Guild questline
Sheogorath - You "help" Pelagius have some self-confidence
Mehrunes Dagon - If you wait too long instead of following Dagon's command to kill someone, that person will attack you, which still satisfies Dagon. But it is Dagon.
Mephala - The quest is fine, but the reward is only marginally useful if you're averse to killing friends
Vaermina - Good only if you let the staff be destroyed, which means no reward
Hircine - Werewolf hunting
Sanguine - Drinking games, although you do fix all the mayhem you cause
Boethiah - Murder
Hermaeus Mora - But seriously, he's trying to get to the Heart of Lorkhan? Also, if you don't like elves this switches to the Good category.
Molag Bal - Torture
Namira - Cannibalism
Peryite - You inhale hallucinogens then wipe out a den of his followers