All The Tropes Wiki Project, Part XV

[Labster]

Or simply Category:Conversations.  Either way, I think what you want should inherit from both Category:Scenes and Category:Dialogue; the latter has a bunch of tropes that should be moved into the subcategory, like:
Breaking Bad News Gently
Easily-Overheard Conversation
Duck Season! Rabbit Season!
Everyone Gets Their Turn (no examples here)
Just Between You and Me
Conversational Troping (the meta-example)
Seinfeldian Conversation
Scheherazade Gambit

Contrast with Category:Speeches and Monologues.  I'm starting to wonder if the whole of Dialogue should be a container category, but I'm not yet sure what the subcategories would be.