If you are just looking for a marriage record and possibly a death record, and both occurred within the City of Buffalo, you can request them yourself, from the city.

Turnaround is quite fast.

Here's a link to the NY State Health Department section that handles genealogical requests. There is a form you can download from the site, and send in.

Make sure you send it to the City of Buffalo, and NOT Albany. The Buffalo address is on the site, too.

http://www.health.ny.gov/vital_records/genealogy.htm