I finally gave up on ordering genealogical records from NY State. They cashed my checks back in July and still have yet to send me any records. I wrote a letter complaining, but I'm sure that will do no good.
So instead I've been emailing and writing various town clerks to see if they might have any vital records.
The Lockport Town Clerk found the death certificate for my wife's great-great-grandfather, John Morris. It's $11 for the death certificate but they charged no search fee upfront.
The Kenmore Town Clerk found the death certificate for my great-grandfather, Samuel Wilson. Again, no search fee. Just a $22 fee for a copy of the death certificate.
Now I'm hoping that this will have the names of his parents, specifically his mother. I have that his father, my great-great-grandfather, was David Wilson, and I even have what's thought to be a photo of David. What I'm unsure about is the name of his mother. It could be Elizabeth Watts. I'm also hoping that it will confirm both his birth date and his home town of Ballymena, Ireland.