That would depend on what follows next and what you wanted to emphasise.
1. The gradual nature of the rise.
2. The rising nature that was gradual.
This is a case of where English is flexible and some speakers prefer one way and other speakers prefer the other way. Also for some strange unknown reason many books and teachers in foreign lands teach that English only has one way when in fact for many occasions either way is perfectly acceptable.
"From 1980 to 2000 two genres such as action and animation were gradually rising in popularity, to reach a plateau of popularism peaking in late 1999."
"From 1980 to 2000 two genres such as action and animation were rising gradually in popularity, to reach a plateau of popularism peaking in late 1999."
Of these two sentences I think sentence one seems better for the context. The popularity gradually rose. therefor it was rising gradually.
But it is just a question of semantics and what different people consider significant.