mem286, as you can see from the examples you gave, some use "Argentine" and some use "Argentinian" for "of Argentina". In my life, the only person I ever heard use "Argentine" in everyday speech was herself from Argentina. She pronounced the i as in "hay" of Spanish. I was a little uncomfortable trying to choose, so I just avoided the subject. Some dictionaries define argentine only as silvery (
http://www.merriam-webster.com/dictionary/argentine ). Perhaps you can enlighten me as to what you prefer. After all, China told us to quit calling their capital Peking and we did. They ought to be the authority.