I don't think there is any true intended way to deal very much of anything in this game. So many different options. I for one train my vampire into a legendary fighter and deck it out in candy. Then I'll usually lead him to cage trap that has been webbed or make him lose his balance and get trapped. Build a tiny structure out in the wilderness with him caged inside and a lever connecting the cage. I like to imagine the look on the goblins faces when the bridge opens, the cage springs apart, and a demonically powerful vampire legendary warrior dwarf comes flying out and tears them apart. The cage system is a bit over the top. I may just end up making his station out there a tower of death. Have levels of lower tier weapon traps heading up to the top where the vampire is a book keeper forever, but does it as an offduty soldier fully decked out in candy. Although perhaps I should just let him have steel. That way if he somehow falls in battle I can pull the switch the open the magma reservoir above the tower. Can't let the goblins get their greedy hands on the piles of business ledgers and stock information that must be piled around the vampires office.
Another option I have done is seal him off in a room with all sort of different workshops. Then pit material from above like all the stone. Then have him endless craft things for me. Then I have him pit all those crafts down by the trade depot. Either that or use locked doors or bridges to partition off a stockpile that he can store thing in, then block him from it, and have the rest of my dwarf forces gather it all up. The vampire is the perfect worker like this. Just make sure his home is covered in high quality furniture and every inch is legendary engravings and he will be fine. Once in a while you can feed him a dwarf that just won't stop tantruming. Imagine that dwarfs face as he's burrowed into a room, the door locks behind him, and a bridge lowers to reveal the nightmare horror just waiting for him to fall asleep.