WRONG.
RASULALLAH HIMSELF (SAWS) made duah against muawiyah. Therefore cursing him is not.outside of Sunnah.
This is confused. Perhaps your mind has been mixed up by the Twelver Shia who brainwashed you.
There is no evidence that the Messenger of Allah, Allah bless him and grant him peace, sincerely made any supplication against Sayyiduna Mu'awiya, may Allah be pleased with him. How could he, when he even refused to supplicate against the pagans who injured his blessed face at the battle of Uhud, Allah bless him and grant him peace? Can we expect that someone who refuses to curse those who are trying their best to kill him will then utter a curse on someone who is merely not responding to his call? This interpretation our Zaydi friend has given is is ridiculous.
As for the statement "May Allah not fill his belly", this is just an Arab expression, which is not meant literally, and can't be understood in the way our Zaydi friend wants us to do. It is similar to expressions like "May your mother be bereaved of you".
As for the claim that the supplication was answered, this has to be rigorously checked so as to steer clear of Mu'awaiya-hating fantasies spread by the Rafidis. Even if it was answered, though, the fact is that expressions that are not seriously intended by the speaker can, sometimes, be answered! This is why scholars warn Arab mothers against saying things like "May I be killed for your sake!' to their children who are ill; even if not meant literally and are merely expressions of compassion, such expressions can be answered, (if uttered at the time when prayers are answered). Such an answering of an expression not meant literally is even more likely in the case of a prophet, peace be upon them all.
It may be that it was precisely in order to deal with the possibility of such expressions being answered and harming the believers that the Messenger, Allah bless him and grant him peace famously prayed that his "curses" be made a source of blessing for the believers.
And it is easy to see how this "belly curse" could be a blessing, even if answered! It is an indirect confirmation of Prophethood after all!
This is a big topic, and this thread is probably not the right place to go into it. I just wanted to make a few points, so that nobody can be misled by the RIDICULOUS idea that "cursing Mu'awiya is a Sunna".