I've been playing this game on-and-off for a while and have been able to figure out most mechanics by my own experimentation, but this is one I haven't quite figured out. It seems like there are a lot of potential variables, and it might be as simple as raising relationship with the target by a few points, or as difficult as acquiring a lot of prestige, or as arbitrary as just trying several times until the dice rolls in your favor. Can anyone present a general guide on how to acquire vassals peacefully?
Hold the natural liege title of the area he is located in and at least one province there too. They will eventually seek your protection. It might take a while though.
As for asking for them to become vassals, it helps a lot to do the above, or at least hold provinces that border his. So if you are the Duke of Holland, there is no way the Count of Pskov is going to pledge to you, no matter how often you ask. You also need to be prestigious, for him to consider you. Good Diplomacy rating is a must too.
Generally though, it is hard to get them to become vassals on your request. Also remember that you get BB for every province he brings along with him. So if you vassalize the Duke of Saxony who holds 6 provinces and have 6 more under rule of his vassals, you'll get a nice 12 point BB increase.
If he offers to become your vassal, you gain no BB. Which is why it is often best to let him come to you. If you hold the right territory, he will.