Adam Rice has come closest to addressing the "Wiener" vs. "Viennese" issue, but has got it backwards. In German, the letter "W" is pronounced as an English "V," hence "Wien" is pronounced somewhat like "Veen," and the adjective "wiener" is pronounced more or less as "veener."

Anglicized, the term "wiener" has taken on its current english pronunciation ("weener"), but that has come to be known as a noun referring to a specific food, not the english version of the adjective "wiener." So there are three options when referring to the troublesome coffee name:

1) Wienerkaffee (would be German form, pronounced more or less "veenerkaffay").

2) Wiener coffee, with "wiener" pronounced with a "V".

3) Most likely, just "Viennese coffee".

(My fiancée, having just read this post, has said, "You know who the wiener is? It's *you*." Guess I have too much time on my hands!)