I spent half an hour doing Google searches and still couldn't find anything more than online schedules for annual graveyard Masses in various parishes in Ireland. Since they were held yearly for the public, they obviously weren't a service for one individual. Finally on Google Books I found, "The Community Life Of Older People In Ireland", written by Carmel Gallagher in which I read this -- "Another ritual that takes place in many towns and villages is an annual graveyard Mass. Family members gather at the graves of their deceased relatives while an open air Mass is celebrated."
What a lovely idea! I can't imagine why this custom is not followed here in New York. In my mind's eye, it conjures up a powerful image of the Mass offered in the midst of His creation, in the presence of one's ancestors and loved ones who have passed, spiritually connecting all. It also puts me in mind of the outdoor Masses celebrated during penal times, when secret Masses were said for the faithful in remote, out of the way places to avoid detection. No mention was found online of how or when the observance of graveyard Masses first began, perhaps if this post falls under the eyes of a reader in Ireland, they could enlighten me.
Curious if this Mass was perhaps celebrated here in New York years ago, like the "months mind Mass" and simply fell by the wayside, I did a search using "graveyard Masses" and "New York" as the search terms, which produced no relevant results. After substituting the word cemetery for graveyard I found two Masses, one in Buffalo, NY and the other near New York City. However, the Mass in Buffalo was celebrated inside a mausoleum, hardly the same effect as Mass said under the Lord's blue sky. Clearly this is not a widespread practice in New York--but I think it should be.