With this word in the news almost every day at the moment, we are hearing two pronunciations from British broadcasters: /ıˈreınıən/ and /ıˈrɑːnıən/. The first of these is, I think, the majority pronunciation, but the second is heard from many who would probably consider themselves better informed about the country and its people – for instance John Simpson. He and I crossed swords over this, and he alluded to our disagreement in one of his articles nearly thirty years ago, ending “He [i.e. GP] walked on, a disappointed man”. His arguments in favour of /ıˈrɑːnıən/ were two: that it was the pronunciation used by Iranians themselves (but as I pointed out, they are speaking English as a foreign language, and so not to be completely trusted on this – just as a Frenchman speaking English but pronouncing his country name with a nasalized vowel would not be copied by native English speakers); and second, that as the country name is /ıˈrɑːn/, then he was simply adding /-ıən/ in the normal way. I countered this with the example of Panama, which also ends in /ɑː/, but whose derived form is /pænəˈmeınıən/.
I was not trying to persuade him because of a belief that /eı/ was intrinsically the ‘better’ vowel to use, but so that he would conform to the one being used by the majority of his colleagues, and so be less conspicuous to listeners and viewers, who would otherwise start asking themselves (and me!) questions, and stop listening to the content of the report, which is far more important.