NOTE: I am ignoring all quest requirements/pre-quests (Many of these require quests that give prayer as well). However ones that I know require defence experience (either to kill a boss or from pre-requisite quests will be marked with a ^ and quests that give/require over 15k defence experience total [ie; including subquests] will simply be striked out.
(I have included quests which give/require over level 44 prayer even though that is what your target is. This is purely as I wish to use this list elsewhere)
XP (lamp/tome/etc) Quests:
Swept Away: 10 portions of goulash, each one granting xp equal to 10 times your skill level for the skill of your choice (100 - 990xp)
Myths of the White Lands: Lamp granting 500 experience in any skill (500xp)
Meeting History: Tome granting 2 x 1000XP in any skill over level 25 and 500XP in any skill over level 25 (500 - 2500xp)
Darkness of Hallowvale: Tome of Experience, giving 2000 experience in any three skills over level 30 (2000 - 6000xp) ^
A Fairy Tale Part II - Cure A Queen: Xp lamp (2500xp to a skill of your choice) ^
Legacy of Seergaze: Tome of Experience, 2nd Ed - 3 chapters of 2500 experience each (2500 - 7500xp) ^
King's Ransom: Reward lamp granting 5000 experience in one skill over level 50 (5000xp) (gives 33k defence experience as a reward).
Great Brain Robbery: Blessed lamp, giving 5000 experience to any one skill at level 30 or higher (6000 - 11000xp [6000xp normal reward, 11000 if the lamp is used on prayer in addition]) ^
One Small Favour: 2 Lamps, each when rubbed grant 10000 to a chosen skill over level 30 (10000 - 20000xp)
Troll Stronghold: Two reward lamps, each granting 10,000 XP in a level 30+ skill (10000 - 20000xp)
The Temple at Senntisten: One XP lamp giving 23000 to any skill, two XP lamps giving 20000 apiece to a chosen combat skill over level 50 (10000 - 33000xp [10000xp normal reward, 33000 if the lamp is used on prayer in addition]) ^
Recipe For Disaster: A lamp to grant 20000xp in a skill of your choice over level 50 (requires total completion of the quest which requires Legends quest)
Nomad's Requiem: 70 Soul Wars Zeal (151200 - 302400xp [Range that can be received from 70 Soul Wars Zeal]) (Requires King's Ransom)
While Guthix Sleeps: Stone of Jas awakening, granting 4x100000 experience in skills over level 65 (100000 - 400000xp) (Requires level 65 defence, minimum)
Blood Runs Deep: Fremennik combat training, granting 3x150000 experience in combat skills over level 75 (150000 - 450000xp) (Requires completion of all Fremenik tasks which require level 40 defence, minimum)
Legend's Quest: 7650 - 30600xp (Just No.)
Quests which give Prayer experience specifically as a reward:
The Restless Ghost: 125 - 1125xp [gives five ancient bones that each give 200 Prayer XP]
Rag and Bone Man: 500xp (additional 5000xp if you do the wishlist)
Making History: 1000xp
Recruitment Drive: 1000xp (Would recommend doing this for xp as it allows you to wear initiate if you decide to get defence)
Priest in Peril: ~1406xp
Fur 'n' Seek: 1500xp (additional 7000xp if you complete the second wishlist)
Mountain Daughter: 2000xp
Land of the Goblins: 2000xp
Ghosts Ahoy: 2400xp
Another Slice of H.A.M: 3000xp
Spirit of Summer: 5000xp
Missing My Mummy: 6500xp
Dealing with Scabaras: 7000xp
Rum Deal: 7000xp
Spirits of the Elid: 8000xp
Summer's End: 10000xp
Swan Song: 10000xp
Holy Grail: 11000xp (gives 15300 Defence XP)
^:
Darkness of Hallowvale: 4600 Defence XP (From Quests: In aid of the Myreque [2000], In search of the Myreque [600], Nature Spirit [2000]).
A Fairy Tale Part II - Cure A Queen: 200 Defence XP (From Quest: Nature Spirit [2000]).
Legacy of Seergaze: 4600 Defence XP (From pre-requirement quests to Darkness of Hallowvale [see above]).
The Temple at Sennitsten: 12000 Defence XP (From Quest: Defender of Varrock [10000], What Lies Below [2000])
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Hope I halped? If I'm wrong (most likely am going to be on at least one thing) then just let me know.