Wil acoustic guiar and vocals be loud enough in Central park ?

I have played with small acoustic groups for over 2,000 weddings in the NY area.  Some were one the grounds of estates where we could use some subtle amplification - and also a digital keyboard.  Others - all acoustic, most often a trio of flute, violin, cello.  During a quiet ceremony, and we will assume a small amount of attendees, you can be heard.  During dinner and cocktails - you become background music, audible only to those nearest to you.  This has to be made clear to the client ahead of time.  If the specific spot in the Central Park does not have the usual tourist/visitor traffic thru it, and is pretty music reserved for the wedding only - you might - might . ..  - be heard well enough.

You might be able to get away with a SMALL unit, run on battery power, that gives you some sound enhancement - but now way is a Marshall stack going to be un-noticed.

You warned them about the possible volume issues. If you haven't already then get it in writing - the party know that the venue is noisy and that amplification is impossible. If they still think it's not loud enough then that's just tough.