The materials are not as hard as you would think, any good smith can manage its creation and mining is not a problem as under frequently build high quality fortresses so mining is not beyond them.
The Lure of wealth or immortality is more than enough to tempt most men, men of science are no different.

You forget as well the entire eastern boarder to Sylavania is mountainous filled with old abandoned dwarf posts and mines, they have the geographical wealth as well, you have to remember they are looking for iron, not gold and silver, its mines are not nearly as rare.
Weapons taken from the battlefield is also another option which would likely be fire with perhaps damaged or destroyed wooden carriages which can be repaired or replaced, its only the gun itself that is of import.
Even if they were melted down and reforged it would at least supply the raw resource.
So we have established they have the raw resource, the knowledge base and man power.
Maintaining them is not all that hard, look at the old Ogre ones... Cannons are very tough and built to last in all conditions for hundreds of years without difficulty.
However the main issue for the Vampires in this case would be acquiring the materials to make the powder... In any sizable quantity it would be extremely difficult so smugglers, bandits and battlefield pillaging will likely be the best option here.