You might actually be able to find these newspapers in the US, depending on where you are located. About 10 years ago, I did a lot of research from German newspaper articles that were housed in the New York Public Library and got help from librarians both at Harvard and Yale in tracking down the text of West German political speeches between 1945-1989. I remember there was a microfiche roll at the NYPL that had all the copies of this publication called 'The Bulletin' which was an English language newsletter from the West German government that reprinted a ton of speeches and news.
I would suggest talking to a librarian in your local library about how you might get your hands on the text of this speech. A good librarian may be able to refer you to colleagues at other libraries with deep German language and culture collections, help you with ordering copies of newspapers through interlibrary loan, show you some databases for newspaper article searching that you might not be familiar with, and perhaps have access to books of speeches or have knowledge of JFK ephemera collections in various archives.
To generalize, library websites in Germany (and in the US, for that matter) tend only to scratch the surface of the collections they hold e.g. some libraries only have books printed after 1990 in an online catalog, so anything printed before 17 years ago is located in a card catalog (unbelievable). This is especially true for materials that might be located in archives, where only a very tiny percentage of primary sources have any mention on the web (archives don't have the money to digitize everything, though we're trying) though there are hundreds of indexes to those sources in filing cabinets in the reading rooms of those archives.
Some useful catalogs of books at German libraries which might help you find printed copies of speeches:
www.kobv.de (union catalog for Brandenburg and Berlin)
www.kvk.de (union catalog for Germany, Austria, Switzerland - the interface is painfully bad but the search is useful)
www.zdb.de (shows which libraries in Germany have various newspapers, magazines and journals)