My maternal grandparents were married in Buffalo in 1926, and their parents are listed. THEIR parents were also married in Buffalo, in the 1890s, and the parents are listed on theirs, too (including maiden names).
Basically, just 3 records prove all my mother's grandparents, and great-grandparents. In fact, one of my gt-gt grandfathers on that side was widowed, and he remarried - I think HIS marriage record is my only record to show what HIS mother's maiden name was.
For early years, you have to cautious about vital records in NY state, because the big three cities - NYC, Buffalo, and Albany - had different rules and might be kept separate from the rest of the state.
Buffalo has a city archives you can call for older records. They're set up to deal with genealogical requests. For copies, you still have to go through the regular office, but they contact them for you and get you set up.
For marriage records like you're speaking of, I always go to the main library downtown, and look at them on microfilm in the local history section (the "Grosvenor Room"). They have the early birth records on microfilm, too, but it's a brutal experience to look one up (it can easily take an hour). Those early birth records are ordered by when the birth was REGISTERED, and so there barely any order at all, and your record can easily be days (or even weeks) away from others for that date. Nobody has ever found my grandmother's birth certificate, although it should be there. Oh, and the handwriting is BRUTAL, too, and often the baby wasn't named at birth, so you have to look through the parents' names.
Anyway, if you're in the area, or are inclined to travel there, the Library is the way to go - you never know if some civil servant is just going to screw it up, especially since it's older than they're used to dealing with, and they probably just look at it as a pain in the butt they shouldn't have to do. If you call the Grosvenor Room at the library, they might be able to do it for you for a fee (I don't know if they do that, but I've heard of other places looking up obits for people), or know of somebody who will.
Or call the city archives, like I said. Don't subject yourself to just dealing with the non-history bureaucrats.