Is there any specific area in the cavern of the stolen fayth where I can find tonberries?

I don't think that there is a specific place in the game where you can fight Tonberrie's.
Why do you want to fight only Tonberrie's ?

So I can get ten of them for the arena. I have yet to see even one of them.

Make sure all of your characters are hurt enough that they are in the yellow.

Tonberries have a tendency to attack injured people. ;)

Another way is to go to the first four way intersection(2 of the ways are dead ends)and go left you should be in a purple room(I think its purple)you should find tonnoberrys there, I did

Oddly, I heard people are having a hard time trying to find Tonberries...... but those people are the guys who are playing Final Fantasy X: International. O_o;;

Now, I never looked for Tonberries in my FFX:I game, only in FFX. And in FFX, I just got the Tonberry (forgot the name of it... the only used commonly with the AP trick) in battle arena without having to look for them. Maybe it's because I went around the Omega Ruins a lot. o_O

(Note: FFX = Final Fantasy X US. FFX:I = Final Fantasy X: International JPN.)

I figured it out. Tonberries only appear in areas where the floor is green. Weird.