In theory, you could find a strong Greek typeface that contrast with Zapfino.
But, for one, Zapfino tends to steal the scene from pretty much anything and, on the other hand, I don’t think that contrast is the best way to match typefaces for a wedding! ;-)

One of the few swashy scripts that support Greek is Champion Script: http://new.myfonts.com/fonts/parachute/pf-champion-script-pro/

Alternatively, you could find several less flamboyant typefaces still suitable for a wedding:
http://new.myfonts.com/search/elegant+charset%3Agrk/

It's for a birth announcement so I was thinking of using Zapfino for the name of the girl, obviously the most important element of this piece. But you would suggest a different font? I like the look and feeling of Zapfino, swashy but not too swashy, hard to explain, totally different from a font like Champion script or Bickham script.
Just discovered the combination of Zapfino (Dutch) and Rotis (Greek and Dutch) seems ok at first sight.

Sorry, don't know how I ended thinking it was a wedding...

Which Rotis, by the way?

Rotis semi serif.
I was thinking of using a non serif like Frutiger but that made it too modern.