Was the pregnancy unplanned by any chance? I'm having similar problems with the father of my unborn however me and him aren't together. This is very difficult for him also and probably hard to process. He probably isn't sure how to tell people.
Just give him time, granted time is running out before you start showing but you just need to sit down and talk like adults and ask him to explain why he doesn't want people knowing, afterall he can't hide if forever. If he's willing to stay around for the baby, go easy on him, hes probably scared.
Has he said why he doesn't want anyone to know???