How to kill Black Dragons?

Well, if you play on the highest difficulty, yes, but what's the point? The AI is still pretty dumb. I don't know about others, but I don't like starting with zero gold just to prove how awesome I am; it seems pointless to me.

I feel the same way; I mostly play when you start with 5,000 gold.
I'll try to write down how you can defeat them using Death Knights, just a theory; I don't have time to test it right now. Let's say you have a Necromancer, a Death Knight, 5 Dracolichs, some Vampires, Cerberuses, Skeletons, and Imps in your army. So, the Death Knight only drinks Health Potions, and that's it. The Necromancer casts Vampire Touch on a Dracolich (should already be level 4 in Death magic). Everyone else uses the "Wait" command. The Death Knights fly towards us and try to take out the heroes. We don't care about the Necromancer because he's already done his job. The Death Knight tries to survive by drinking potions and tries to take out the Death Knights by taking damage (e.g., hitting one soldier first so that there's no retaliation). Then, we just attack them, and that's it. I'll definitely test this later.
By the way, I'm not sure, but it seems like "Hand of Death" works on heroes with 100% magic resistance; maybe it will work on Dracolichs too? You can also use the Necromancer's "Sacrifice" spell, but that's level 5, and he probably won't survive that long.