I have a few ideas (as a dwarf player) but could do with a few specifics.
Although Dwarfs will have magical war machines, an artillary heavy army will be unlikely to have too many magical waepons. If you throw in a unit of 2 of spirit host you should be able to hold up some of his shooting for quite a while, and quite possibly beat them eventually (units such as thunderers ets...) Wraiths could also be a good idea but I'd leave the Banshee at home due to Dwarf's high leadership.
spirit hosts are pretty pts heavy though - especially in games under 2000pts since you're already likely spending at least a good 500 pts on your characters...
the ethereal stuff will simply destroy any missile unit, but if those war machine are decked out in runes, they'll instead have a field day killing your ghosties!!! unless you know his war machines aren't magical, i'd probably play it safe and keep the ethereal stuff at home...
now a black coach used well could work! yes the dwarves can put lots of S7 on the board, but the coach does come with a ward save, and it causes terror! with a little luck and a screening/diversion unit, the coach could walk through the dwarves rear lines quite easily!
Its a bit of a dirty trick this but Ghoulkin + Flying Vampire equals a dead war machine on turn one (most dwarf generals leave an Organ Gun at the front of their lines, should be target number one). The Vamp can then either go back to a unit or play the risky game of flying around terrorising the war machines. Note: NOT YOUR GENERAL!
the better way to run it is;
vampire w/infinite hatred + ghoulkin. talisman of the lycni, sword of battle, armour of the night or flayed hauberk.
flying takes too many bloodline pts, and it's dead handy to have the re-rolls in case you flub your dice... you've still go an 18" charge range, but with the armour of night you're also harder to hit! at best your opponent is -3 to-hit you with all missile weapons - just beware of magical missiles! (not an issue against dwarves obviously!)
another varient which i've been using lately against a high elf gunline is;
vampire w/infinite hatred, avatar of death (additional hand weapon). wristbands of black gold, talisman of the lycni.
i'm actually likely this guy even more! he's got a nifty 3+ ward save against shooting & magical missiles so he's even harder to gun down! you'll just need another vamp w/ghoulkin to help 'slingshot' him into combat turn 1... (or you could just wait a turn!)
Fell Bats!!!! Turn one, Vanhels them straight into the nastiest looking machine, outnumber him by fear, win. One down! This could be combines with a flying vampire to neuter a lot of things very quickly.
Dire Wolves. Only 40 points, they either distract him for a bit of shooting or they sneak round and start playing with the machines.
totally agree about the fell bat idea! against a gun line, i'd say go with a unit of 5 - especially if you can't spare a vampire w/SCotN power to sit nearby them and keep healing them...
the dire wolves however aren't so hot at anything beyond screening/redirecting... they're pretty poop all round in combat against pretty much everything! they can likely keep a war machine occupied for a few turns, but you will lose them against dwarven crew unless the dwarf player flubs his/her dice rolls...
Although it would seem tempting to go with Heavy Cavalry units I would advise against it. Blood and Black Knights are expensive and will be torn to pieces by the inevitable Organ Gun(s).
actually, black knights if used properly can be disgusting against dwarves! (blood knights are out though untill you can spare the pts for the banner of blood keep and a vampire to babysit them and res them back!)
remember, black knights move like ethereal models! don't give them barding as it only slows them down. run them up into forests, keeping them more than 2" in if you're not setting up a charge, otherwise of corse keep them within 2" of the edge of the terrain! or else hop them behind a solid building or some such obsticle... you've always got vanhel's/book of arkhan for magically charging them too!
Thats all I can think of for now. Dwarfs aren't the easiest match up for vampires but you should be ok.
dwarves are actually a fairly easy match-up for vamps, if you build your army right. like high elves, dwarves are solid at dispeling magic, so a few basic rules apply;
- take 2 vamps w/dark acolyte in games under 2000pts. if possible, try and work a 3rd vampire in there, or a necromancer.
typically against dwarves & high elves, i try to make sure i get at least 6-7 power dice/phase in games under 2000pts, while in 2000-2250pts games, i'll aim for 10-11 dice to ensure i can get the important spells off!
- a corpse cart w/unholy loadstone can make sure you get the most out of your summon spells, and will help if one or two of your attempts get dispelled.
- take bound items. we have lots of nasty bound spells available! use those first to suck out some dispel dice, maybe even a scroll if you're lucky!
- stick to either skellies or ghouls for your core. it's easier to raise big units if you can concentrate on summoning just a single type! untill you hit that magical 2000pts mark, you don't want to spread your invocations between skellies & ghouls as you won't have enough power dice...
- the nightshroud will turn any vampire/wight king wearing it into a killing machine! it's also a solid item for your general at lower pts values as it lets you get the drop on anyone trying to assassinate him!
posting your army list you've been using and if possible a brief rundown of your opponent's list will also help us suggest ways to beat your stubborn opponent!