Are there any quests for the Eight/Nine Divines?

AEDRA

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:

Dibella
Kynareth - Weak albeit unique reward. Unless you like saving trees. A lot.
Mara

AFAICT the following have no proper quests:

Akatosh
Arkay (aside from a minor fetch quest in Whiterun that nets you a pittance in gold)
Julianos
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)
Zenithar

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DAEDRA

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:

Probably fine:
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

Ambiguous:
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

Questionable:
Hircine - Werewolf hunting
Sanguine - Drinking games, although you do fix all the mayhem you cause

Evil:
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

There is 1 daedric quest for every daedric prince with the sole exception of Jyggalag. So in total there are 16 daedric quests. Every quest will involve the daedric artifact of that prince in some way.

There are only two quests for the Divines (Technically "Aedra", but they are always referred to as "Divines" in dialog):

The Heart of Dibella

and

The Book of Love (Mara)

The other six (+1) Divines do not have associated quests in the base game.