The Golden Primal Direhorn is exhibited in the header image for your delectation, and he is available, just like his Crimson Primal Direhorn brother, from gaining exalted reputation with one of the new reputation grind factions -- the Kirin-Tor Offensive for the Alliance's Golden Primal Direhorn, and the Sunreaver Onslaught for the Horde's Crimson one.
There are several other Direhorn mounts available, all of these are Primordial rather than Primal, and come in four different colors: Amber Primordial Direhorn, Jade Primordial Direhorn, Cobalt Primordial Direhorn, and the Slate Primordial Direhorn.
All of these mounts drop, at rather a low rate, from Zandalari Warbringers, which are found dotted around Pandaria with patch 5.2. These guys are distinct from the lesser Zandalari Scouts in so much as they are riding the Direhorns already, and rumor has it that they drop the color direhorn they are riding. These Warbringers, having brought one down myself on the PTR, might be solo-able by the right class with the right gear, but are very easy indeed in a small group of two or three.
Raptors are back in a big way in patch 5.2, with a whole island dedicated to them. The Black Primal Raptor is another Green Proto-Drake. It drops from Primal Eggs, with a relatively low drop rate, and you have to wait three days for your egg to hatch, just like the one from the Oracles. However, it appears that there's no reputation required to obtain the eggs -- they drop from mobs on the Isle of Giants, allowing you to combine your Black Primal Raptor grind with the one for the next mount on our list.
The Bone-White Primal Raptor is a quest reward, but it's quite a quest. As WoW Insider reported, the Bone-White Primal Raptor is obtained from A Mountain of Giant Dinosaur Bones, from Ku-ma the Bone Collector on the Isle of Giants. This quest currently requires you to collect 9,999 large bones, from mobs that drop around 4 bones per mob. So, you'd have to kill around 2,500 mobs to get this mount! Ku'ma, the troll who hands out the quest, also has various other things to offer.
There is also a Green Primal Raptor and a Red Primal Raptor in the data, but no word yet on how they are collected. It's possible that these may turn out not to be included, but WoW Insider will keep this guide updated should they appear.
There are various other mounts available which aren't remotely dinosaur themed! Some of the mounts in this section are from as yet unknown sources, if firm information is discovered the guide will be updated.
The Thundering Cobalt Cloud Serpent drops from new world boss Nalak, a world boss who is based on the Isle of Thunder. Accessing this world boss apparently relates to the War Effort on the Isle of Thunder, and the drop rate is extremely low. This mount requires the August Celestials Exalted to ride, for undisclosed and mysterious reasons!
The Sky Claw is a mount crafted by engineers. The initial requirement for materials was extremely high, but has since been modified to 30 Stabilized Lightning Source and 30 Living Steel. The mount can currently also be sold, although given how cheap it is to make this might change.
The Clutch of Ji-Kun and Spawn of Horridon are currently from unknown sources, but it seems reasonable that they might drop from the raid bosses, Ji-Kun and Horridon. The Armored Skyscreamer is also currently from an unknown source, but Wowhead's dataminers recently uncovered a Glory of the Thundering Raider achievement, which awards an Armored Riding Pterrorwing. This sounds very like the Armored Skyscreamer!
The Armored Bloodwing is also from an unknown source, but mount collectors have speculated that it is most likely to be either a boss drop, perhaps from Ra-den, a Scroll of Resurrection mount, or even a mount associated with something like a guild level achievement or sourced from Blizzcon. No Alliance version has been found so far, implying that it is not faction-specific. Wowhead's comments contain further informed speculation!
The Ghastly Charger, which was datamined as part of the patch, is actually learned from the Ghastly Charger's Skull, a loot card from the latest WoW Trading Card Game Expansion, Betrayal of the Guardian.