At least this would be more appropriate that what she actually does in the show.

@Background Pony #31F4  
I don’t know if Fluttershy’d be able to pin down the culprit on her own. How sensitive is a female pony’s sense of smell? I suppose she could check everyone’s behinds, but that doesn’t sound like something Fluttershy’d do. What she might do is bring in a fox or wolf, passing it off as a creature friendship lesson, to make the determination.
 
If she could identify Cozy Glow as the one that made the mess, then yes, she’d likely put her in a diaper. Then, curly pony gets what she wants.

@SinnerWhoKeepsTrying1978  
No. Flutershy notice and put her in diaper

I’d give Glimmer the following advice, that she not be surprised if, should she refuse, she hears a conversation on the lines of:
 
Gallus: Yona, you won’t believe what happened in class today.
 
Yona: What happen?
 
Gallus: Before Miss Fluttershy showed up, that one winged filly, the one with all the curls, she was there early, like usual. Well, she flew out of her chair to the back of the room and said, “Hey, everypony, I’ve got this real amazing thing to show you. I bet nopony else can do it.”  
We didn’t know what she was talking about, so we went to the back of the room to see. Next thing we knew, she was peeing all over the place.
 
Yona: Yuck. Why curly winged pony do that?
 
Gallus: I don’t know. You’d think she’d know by now that every creature can do that. Anyway, I didn’t want any pony pee on me, so I jumped out of the way. Then, when she was done, she said, “That’s not the best part. Let’s see if anypony can do this.” And, she started pooping.
 
Yona: Yona remember when Yona younger, Yona pee and poop in front of other yak, think only Yona do. Yona learn other yak also pee and poop.
 
Gallus: Her poop landed in her pee, splashed all over everyone. She was done pooping and back in her chair just before Miss Fluttershy came in. We all were, back in our chairs, that is.
 
Yona: Yellow pony not notice smell?
 
Gallus: She did notice. She thought some creature had just had an accident, and called in the janitor to clean it up.
 
Yona: Why not re … re … why not tell yellow pony about curly pony?
 
Gallus: I’m not a tattle tale. Someone else can report her.

Classroom have carpets. She wet on them

@Background Pony #31F4  
That’d likely be easiest for her to do. And, if the floors are slippery when wet, it’d also be the most dangerous, as long as there are no carpets. Knowing Cozy Glow, she’d likely at least try something like that.

@SinnerWhoKeepsTrying1978  
Wetting all over school

I wonder if she has a particular threat in mind if she doesn’t get her way.

@Wiimeiser  

Not you again…

@northern haste  
Who says she’s getting paid?

Sg: whatever twilight is paying me it’s not enough