Maybe never

You don't say when in September you want to go, or for how long, but I found standard seats on the non-stop DL flight JFK-FCO on the 9th and returning on the 23rd with a combination of AF/AZ no problem. Search the CO site using NYC as the deaparture point instead of EWR and you should see it all. Plenty of other return dates were also available, as were J options on some routes.

Also try http://www.nwa.com/jp/en/home.html for searching NWA/KLM options.

PS - Welcome to FlyerTalk!