Until now,this is what I know:
Based on the Social Security Death Index, found by searching on ancestry.com, I know that my great-grandfather, Angelo Palmeri, was born 27 Jan 1886 and died in Sep 1969. Based on census records, I know that my great-grandmother, Maria (Giambrone) Palmeri, was born abt 1891. I know from talking with with my dad that she probably died somewhere between 1970 and 1975.
I try calling Holy Sepulchre Cemetery in Buffalo, where I know my grandfather is buried. Maybe his parents, my great-grandparents, are buried there as well. No, they're not. But the cemetery suggests calling Mount Calvary, which is right across the street.
I call Mount Calvary. Sure enough, they're buried there. Awesome!
They can tell me that my great-grandfather died 29 Sep 1969 at the age of 83 and that my great-grandmother died 11 Jul 1972 age the age of 82.
Unfortunately, they have no record in the office about their birth date. But they give me the location of the grave site.
My sister takes on my mission to find their grave. With some calls back and forth, including some searches of google maps by me while on the phone with her, she locates the grave marker and sends me a picture:
gravemarker for my great-grandparents, Maria and Angelo Palmeri
Maria (Giambrone) Palmeri was born in 1890. I don't know the day or month, but this narrows things down a lot from where I was only yesterday.