Well, "darkest story" is pretty tough to define... Each individual has his own themes more dark than another. There can be small dark moments, or general dark atmosphere...
Many LBT sequels had that in them, actually.
II has first true villains and their horrific actions.
III, possibly, has the most dark general atmosphere, from beginning till the end, with all this situation with water during all the movie, worse conflicts between herds, near-death of Great Valley and its residents because of lack of water and fire, and then situation repeated in Mysterious Beyond.
IV has theme of near-death of your close relative, and very dangerous travel to Land of Mists.
In V herds left valley because of danger of hunger, travel through lifeless land again, with more conflicts between herds, each time Gang stepped into Big Water something very bad happened, their parents for a long time thought their children could be dead.
In VII we have horrific Pterano's backstory and his relationships with other herds, and his actions, together with two villainous accomplices, make situation nearly repeat again.
In XI herd of tinysaures was hunted down during all the movie, because... you know why.
And that's just some of them I can tell about right away, without deep thoughts, and I didn't list some other movies, though I can say something about them as well right now.