correct

The groom and the bride are sitting in front of guests. They are very wonderful happy.

Wonderful isn't normally used like that.

You normally tell someone they're being wonderful, or the trip was wonderful, but people don't normally call themselves wonderful or have it used like this. Although I guess it is correct english?

correct

The groom and the bride are sitting in front of guests. They are very wonderful.

Yes it is all gramatically correct, however as John Smith said, 'wonderful' does sound a little strange used in this way. 

Yes you can also use beautiful, however beautiful usually (but not always) refers to appearance alone, if that is what you mean.

You can place any adjective in that spot and it can be used.

They are very wonderful.

They are very lovely.

They are very zesty.

They are very splendid.

They are very disfigured.