It seems to be more about Simba learning a lesson so I'd say, him rather than Kiara.

I would say Kiara--Simba would be the deuteragonist.

Kiara and Kovu. Lion King 2 is a "Romeo and Juliet" kind of story, with a happy ending, of course. Simba is an important part of the movie, as the king, the one who denied their love. But he was the protagonist of the first movie. He had told us his story already, It was time for the future generation to tell their story.
And @Crazedsitcomfan : SImba's name in the title, doesn't make him the protagonist. The protagonist is the main character from the movie (here), the one who spends most time on the screen, the one the story is about. And The title "Simba's pride" logically, is about Simba's pride, about what happened after he became king, about the future generation. If you want, he shares the title with Kiara and Kovu.

Kovu and Kiara

Kiara is the main protagonist of The Lion King 2. Simba is protagonist only in the first film.