2 last things I swear!

Shipping a professional army ( as in has the tech or armour to deal with tough units) and sitting on the border of Rome prior to negotiations might help as a last resort. (In my Sicily campaign when I went straight for Rome, I was attempting to do this prior to attacking but the Papal armies blocked me from getting there and were bringing up reinforcements. A stronger navy may have allowed me to do this, in fact ANY remnants of a Navy at the time, heh....)

I think the reason HRE always has good standing with the papal states in my campaigns is because of Bologna's postion being very close to Rome and usually has a full stack army sitting in it. That's why Florence is very contested to hold even after taking it and in good standing with the nearby factions maybe.