For football, after Iowa, I'd say KSU and (embarrassingly) UNI would be rivals. KSU is the Farmageddon game. UNI shouldn't be a rival, however our recent performance vs Purple Hawks had made this more of one due to loud Purple Hawks.
Historically Mizzou and Nebby used to be football rivals. The former was a trophy game and the latter was due to proximity and increased ISU wins over them before they bolted.
For basketball, KU and Iowa would be the main two rivals. WVU is more lately due to their thug play. KSU will pop in when they're good. Historically Mizzou was there before they bolted.