For this particular faction you will have to do quite a lot of world-tour in Azeroth. Most of the quests that give Darkspear Trolls rep are spread out widely throughout the world balancing between Kalimdor and Eastern Kingdoms. Some of the key quests that you could do quickly to gain reputation with this faction are listed below:
1. I had mentioned this above and I will mention this again. Starting zone. A lot of the quests would give reputation for both Darkspear Trolls as well as Orgrimmar. At level 80 you can complete most of these starting zone quests pretty quickly so it is worth the time spent to do them.
2. Some of the quests in Barrens which include Egg Hunt, the harpy chain which leads to Malaka'Jin in Stonetalon Mountains give significant amount of rep. Two quests also can be completed in Malaka'Jin itself.
3. There are two trolls surrounding a cauldron at Grom'gol Base Camp in Stranglethorn Vale. Complete all the quests including the one that leads to Hinterlands.
4. There are trolls inside the outpost of Hammerfall. Completing all Stromgarde quest chains. Further, other quests like the one to kill Marez Cowl and the raptor chain involving Gor'mul and Tor'gan, are worth significant reputation.
5. There is a troll-dominated village called Shadowprey in the southwestern part of Desolace. You can complete all of these quests too.
6. Zoram Strand is another location in the northwestern area of Ashenvale. All of the quests given by them also give insane amount of Darkspear Trolls rep including the Blackfathom Deeps quests that precede after the normal ones.