Is the supplication (duaa) of Yunus, peace be upon him, called “Ayat al karima”? We are getting requests of reciting it for Palestinians and passing it on. Is that established by Sunnah? If not, how may I explain this to the Muslims who argue whenever we oppose their desires?
No, the supplication of Yunus, peace be upon him, is not called “Ayah al karima”.
However, it is a supplication you say when you are upset and there is something burdening you, it is called “دعاء الكرب”. As for these requests to say a specific supplication and then to pass it on is an Innovation (Bidaa). We all should supplicate for the Muslims especially in Palestine and Syria but we do it by ourselves.
Regarding how to deal with these people, my advice to you is to not argue with people who do not have knowledge and deal with religion in their own heads. Arguing with a person who does not talk with proof (daleel), is something which Allah hates.
There is a narration (hadith) which is a pillar and the Scholars prohibit and warn from innovations upon this pillar:
“من عمل عملا ليس عليه أمرنا فهو رد”
“Whoever does an act of worship which is not according to what the Prophet, peace be upon him, and the Companions did, then it will be rejected.”
Believe me, it is easy, clear and simple for those who want the truth (haqq) and, vice versa, it is not understandable for those who want to follow their own minds. Do not waste your time; Give them the proof and stop the argument.