I've played dwarf gunlines a couple of times and found that you either win spectacularly or lose disastrously, there doesn't seem to be much middle ground. It all depends on just how well his 1-2 rounds of shooting go, making dwarf gunlines one of the dullest enemies to face IMO.
I would say that a solid core of ghouls with ghoulkin is a must. The extra move can get you in combat a turn earlier which can massively improve your chances. Ethereal units are good too, generally he will have to fire at them with his warmachines in order to weaken them enough to finish them off in combat, this takes some of the heat off your other units. it is also likely he will have only one or two combat blocks, so the etheral units can quite happily go after warmachines or missile troops safe in the knowledge there aren't likely to be any magical attacks back on them. Bats and wolves are also a good choice as these are threats he must deal with before turning his attention to your main army.
Having good raising ability is a must, you need to keep your block infantry healthy if you are going to beat the dwarves at close quarters. Remember that even a basic warrior unit is a tough nut to crack. Spells like pit of shades or purple sun are a massive help here if you want to go with the cheesy sacrificial vampire route (hey, you're playing a dwarf gunline, throw stilton at him as much as you want). Consider items like the ironcurse pendant as even a 6 up save against his warmachines can be incredibly useful.
One thing I haven't worked out how to deal with is the Anvil of Doom. I've only managed to assassinate it once and that was with wood elves back in 7th ed with the help of some careless positioning on my opponent's behalf. IMO an assassination attempt by vampires is pretty futile, a hero level vampire is unlikely to succeed in killing it (think 1+ re-rollable armour save and immune to KB and poison as standard) and a lord is too valuable to risk. Some spells could work, but most of the spells that could take the anvil out either recquire close proximity and will certainly be dispelled or a suicide vamp who is better off firing purple sun at infantry blocks anyway. It's unlikely to be worth spending so many dice trying to kill the anvil each turn instead of raising/vanhels anyway. My advice is to weather it as best you can until you can tie it up with infantry.
Normally I'm a big advocate of corpse carts, but in this case I don't think they're worthwhile. A Varghulf will certainly attract warmachine fire and may buy you some time, but is probably too expensive for this role. Bats and wolves are a better choice. Zombies can actually be worthwhile here as they are generally considered a waste of shots, but can be raised easily enough to tie up some of his troops. better yet if he drags his anchor (usually a big block of ironbreakers or hammerers) out of position to flank them.
Having said all this, a gunline is still often a game of luck. There's not a lot you can do when your opponent's organ gun rolls a 10 three times in a row :swear:
. I'd pry recommend keeping him out of LoS for the first turn if possible since you can't charge the first turn anyways and if he goes first, then it won't be able to open fire.