Beasts has at least two. By the end of "Next of Kin" when the australopithecines team up to drive off the big cat Dinofelis from a threatened youngster, and when the matriarch of the mammoth herd welcomes the delayed female and her calf in "Mammoth Journey".
Making the ending of "Next of Kin" was that Blue was the Butt Monkey (Incredibly Lame Pun recognized) of the Australopithecus tribe, an orphan who was basically a hanger-on to the tribe after his mother died. The fact the tribe considered him worth saving make it extra heartwarming.
The ending to Walking With Dinosaurs would be a Tear Jerker, except for the very end, which shows (just like ending to Jurassic Park), that even though the giant dinosaurs are gone their smaller relatives — birds — are still with us.
The book version of Giant Of The Skies makes the ending a tad more uplifting (no pun intended) when we learn that the old Ornithocheirus did not die in vain.
Despite this ignominious end, the old male was a success. In his 40 years of life he probably sired several thousand offspring and it is likely that some of them were on this beach, competing and succeeding where he finally failed.
At the end of the film, Scowler apologizes to Patchi for being a jackass to him, and Patchi finally becomes the leader of the herd. Not only that, but he also gets his girl (Juniper) in the end. He really did earn his happy ending despite his rocky start.
Scowler gets an earlier one when he sees Patchi return after kicking him out of the herd. What's the first thing he does? Warn him to keep away from the attacking Gorgosaurus and get to safety.
Patchi rescuing Scowler is another one.
When Patchi enters Heroic BSOD to the point of allowing the scavengers to eat him, Alex refuses to leave his side and convinces him that he should live. Talk about Undying Loyalty.
There are points in "Time of the Titans" where the baby Diplodocus almost sound like they're talking to each other. It's way cuter than it sounds. Also, The baby Diplodocus in general.
Before it went bad, the whole subplot with the Cynodonts in the first episode. In particular...
Narrator: The bond between Cynodonts is extraordinarily strong: they pair for life. (said as the mother and father Cynodont nuzzle)