Hmm, if you don't object to a bit of diplomatic cheese, the best way is to offer them a settlement open ended.

If you openly offer them say Sofia in your example (ie: a border/desired territory), they will usually return the offer saying give Sofia and state their terms. However, those terms will be bad if your relations with byzantine are terrible, despite your good global rep.

If you offer them a far flung settlement thats of no strategic value to them ie: Riga, they will refuse offer. If you then offer another 'useless' settlement to them openly, they will be pleased and usually get a rep boost. However much you repeat this is up to you as it's very easy to get perfect relations. I limit myself to 5 actions/turn/faction, 3 of which may be 'open'.

As you have a good global rep (good show that chap ), this seems to enhance the 'rep boost' although I have no parsing of this it seems to play out ie: at trustworthy+ and perfect relations you can pretty well ask for anything.

However, I find a good way to 'boost' diplomacy is to completely outgun the ai's little autoresolve military brain. ie: if you are wanting a ceasefire, you'll have a heavy stack in the border area with that faction to act as persuasion.

If they have standing armies, I'd give them a chivalrous hoofing first (release) then ask for ceasefire when their standing armies are depleted.

Another way i have found succesful is offer to buy a ceasefire for say 10k florin and 1000/10 tribute but take a territory in exchange. the upfront cash will often entice a poor faction more than it should.

Anyway, have fun with the bartering, I'd start with buying a beard in jerusalem..