IB availability doesn't show up on AA.com and they may have some availability though MAD. I usually check IB availability on BA.com (you just have to sign up for a BA account to be able to search). To book an IB award with AA miles, you'll have to call AA reservations.

There isn't anything else you can do online that shows anything more - it will show what's available for those partners that AA displays online.

But it is too early to see availability for your dates, and picking other random dates isn't necessarily going to reflect what ends up being available for your future dates...though generally BA's fuel surcharges will mean their seats are not snatched up as quickly.

Your best bet, as with any award program, is to be as flexible as you can as with departure and arrival locations and times and keep checking once availability begins to open up for your date ranges. As mentioned above is you're visiting other places in Italy you may want to look at in/out of different cities. Or worst case, even consider taking the train from another city which can be a reasonable alternative if you just can't find anything directly to FCO.