I've used the Perch about 150 times now, and only found 1 fragment. Are there any specific dragons I should use for specific quests (such as quests titled 'Prismatic Rift' or 'Ruins of Alsvitheim') instead of getting the 2-hour-long quests bringing back XP or coins?
As Shadur points out, the game itself give you clues on the elements you need for each quest. If that is not enough of a hint, the DragonVale Wiki has an excellent article on quests which covers dragon recommendations for every quest as well as all of the possible outcomes based on the completion time (so you can know what you are going to get, before the quest completes). If you are finding the quests tedious, remember that you can also use the Dragon Track to get the statue of Kairos.