Does artificially created tensions count? There was that hypnotizing session on AKBINGO/0jin59fun (they're essentially the same thing anyways...) where Maimai and Acchan were fighting over Sayaka
So I guess in a bout of more Matsui Rena bullying, Akimoto Sayaka takes a try at it (from 2009-02-05 AKBINGO!). The girls are playing the fast word battle and Rena is on the Kiyotucky team. When she steps up, she's asked how much confidence she has... to which she reponds, "None!" Sayaka (on the Bossburger team), sensing Rena's weakness tells her to fail from the start! However this is not normal Sayaka since she almost pretends like she didn't say anything until she says it again! Not sure if this really affected Rena or if she was going to fail from the start but as many could've guessed, she did Sayaka, deep down a good person, apologizes with "I'm honestly sorry."
Yes, I posted about that in the Rena thread a while ago. Cool that you picked it up as well
Sata: Are you confident?
Rena: No
Sayaka: she fails before she even started
Rena: *messes up*
Other: It's Sayaka's fault!
Sayaka: I'm really sorry
More Sayaka/Rena tension occurs in the 'lucky girl ranking' episode.
Rena: *gets 4th luckiest* I thought what will I do if I'm in last place...
Sayaka: What is there to be done? (Sayaka hasn't been called at this point so she could be the unluckiest.)
In the case of Rena/Sayaka, I think it's because they just are two different types. Sayaka is much more confident. The Rena/Kojiharu tensions seems more vicious. (well, Rena doesn't care, it's all Kojima being evil haha)
edit: There is also Kojima VS The Kenkyuusei
she steals their candy! (well, she steals everybody's sweets)