Re:NPR Does Roadfood
...or when sounded like "a" as in "neighbor" or "weigh."
Then there is a whole list of exceptions (like "foreign").
And when two vowels go walking the first one does the talking and it says its own name. In which case we would be talking wine-ers.
But these are rules for English (and they don't work very well). "Wiener" (short for "wienerwurst" and meaning Vienna sausage) is a German word. I'm sure the Germans have their own rules.
Not only does NPR spell it "wiener" so do the Oxford English, Merriam-Webster, Random House and American Heritage dictionaries.
Even the Providence Journal spells it "wiener."