First of all, I object to the title of this thread. Rose is not really “annoying”, she’s just boring and pointless. And anyone who says C-3PO is annoying has no soul. 😉
But to answer your question, I’d probably say the battle droids in the prequels. They’re clearly supposed to be funny, but they’re just not. The only moment when I genuinely laughed at them is when that one droid in TPM took 10 seconds to realize that Qui-Gon was the Jedi he was looking for. Other then that, they should deactivate their voice boxes permanently.