What does Tenri whisper to Diana? In episode 12, season 3 of the anime The World God Only Knows, there's a scene at around 5:14 where Tenri speaks to Diana and tells her something surprising. Diana responds by exclaiming why Tenri didn't say anything before.

The next time we see Diana she has wings. 

I'm guessing Tenri told Diana something that would promote their relationship with Keima, because she grew wings, but since Diana has been with Tenri ever since she was a little girl, I'm not sure what Tenri could've told Diana that would be so surprising.
Posting as answer because can't use spoilers in comments, still just a speculation...

With the recent development in the manga, it seems it might be something along the lines of:


  Keima is the one that chose me to be your host 


Also, remember Diana grew her wings once before (although they didn't notice), in manga Chapter 139 (can't remember which episode), after Keima apologizes to her in his library.