Folks I don't have time to further investigate but l was looking to book
travel to Rome and came across this price for several days in march from JFK
to Rome on American Airlines.
I am currently seeing seats in the $45 dollar range for travel from JFK to
FCO plus taxes. Some days the price jumps to an outrageous $70 lol. You
can connect from LHR or MAD but I am sure the MAD landing fees and taxes
will be lower than the outrageous LHR ones.
Anyways I can't find any cheap (under $500 return rates) right off hand but
maybe with a little digging if someone has some time on their hands someone
may be able to work this.
I started my search here.
Link: http://www.aa.com/netsaaver/viewNetSAAverSpecialsDetails.do?fN=
Good luck.