My father is wanting to buy a “Gun” for home defense because of the whole coronavirus chaos, but he obviously can’t buy a firearm. So I’m wondering if he could buy a Black powder pistol legally.
I agree with the other answer, there is nothing obvious about why he can't buy a firearm. Is he an undocumented immigrant? Because if he's here legally, then he's allowed to possess a firearm just as a citizen could.
To answer your question directly, black powder is still a firearm per state law, so if a prohibition exists on regular firearms, black powder is not an exception.
From the facts provided in your statement it is not clear that he cannot buy a firearm. If he can pass a federal firearms background check he can purchase a firearm.