Here is my list of popular Catholic churches in Rome for your wedding. I have included some images and all the contacts for them all. Of course there are lots more than I have listed here but these are the ones I seem to find myself at most. If you click on the names they link to the websites of the churches.
Via Degli Artisti, 41
00187 Roma, Italia.
The contact priest is Father Michael MacCraith.
Piazza San Silvestro,
00187, Rome, Italy
E-mail : firstname.lastname@example.org
The contact priest is Father John Fitzpatrick S.A.C.
Pontificio Collegio Irlandese,
Via dei Santi Quattro, 1,
00184, Roma, Italy
Contact: Alison Mills
Mailing Address: St. Patrick?s, Via Piemonte 60, Rome 00187
Church Address: Via Boncompagni 31, Rome 00187
The contact priest is Father Tony Finn OSA.
Via Venti Settembre 15
00187, Roma, Italia
The contact priest is Fr. Greg Apparcel.
Piazza S. Maria in Trastevere
Via del Velabro 19,
00186 Roma Italia
Piazza Foro Traiano, 89,
Other churches you could look at are, Church of Saint Anne in Vatican and Cappella del Coro (Chapel of the Choir) at the Vatican.