A girl i knew had a small ceremony then invited other people to the reception
She worded the invitation to read that N****and D**** are getting married in a private ceremony on BLAH BLAH and would love for you to help them celebrate at their reception....
something like that

She did offend quite a few family and friends with the whole event, but i think that was more to do with the fact she turned freaking crazy and rude and psychotic and demanding....(another story completely!!!) and not because of the private ceremony thing.

Good luck!