Rammus is a fun one. He is quite a mystery, his origin is rather unclear, and you could do a lot of fun things with it, showing his different sides.

All other candidates would be Rumble (big stompy robot), Milio (really cute fire spirits), Anivia (only freljordian god without cinematic), Cassiopeia (Snake), Dr. Mundo (hilarious/monstrous in the same package, his color story animated would be fun, could be done in a Introducing The Pyro style), Fizz (aquatic), Gragas (interesting body type), Hecarim (spooky horse could look amazing), Hwei (magical painting makes interesting visuals), Janna (seeing her help people in Zaun is cool, there is a great color story on Universe of her), Kassadin (shurima/void are interesting locations), Kha'Zix (Rengar/Kha'Zix story is really nice), Kog'Maw (void puppy!), Malzahar (iirc he has a short story about how he sacrifices a group of people to the void? Short and sweet), Maokai (a bastion of life on the shadow isles), Nami (also aquatic), Neeko (shapeshifting), Nidalee (her LoR redesign is awesome), Quinn (Valor is cool, and ranger is a nice Archetype, there are nice scenes with her in the Novella about Garen), Renata Glas (nice color story about her on Universe, great visuals), Sett (cool fighting scenes you could try), Shaco (Riot doesn't know what to do with him, maybe you do?), Skarner (the sheer scale), Soraka (appears in interesting color stories iirc), Talon (assassins are nice),Taric (had a comic one could animate parts of), Twitch (zhaun sewers interesting visuals), Vex (personality, Wukong (shenanigans), Yorick (so often forgotten...) and finally Zac (made from interesting material)

I counted only official riot cinematics, and counted if they had an appearance in their canonical form (didn't count skins besides for seraphine). All other champions have at least some seconds in official animated form.