I am a New Yorker and have many ancestors in Calvary Cemetery. It became the main cemetery for the Archdiocese of New York tho others have been added since. There are over 1.75 million burials there. They hold a great deal of information.
You can call or, if not in the US, you can write. You can get the location of the grave freely but you must have either the date of death or date of burial. They don't do research. There is a significant cost to get a full interment list, ie, everyone in the grave. Ask how many are in the grave.
If you decide to pay for a full interment list, be sure to ask these questions--who bought the grave, what date did they buy the grave, what was the address of the person who bought the grave. I have broken down walls just with those facts.
Also ask for--which Calvary (they are numbered as land was bought), section, range, grave.
Also ask for them to go to the microfilm for the information. The later records have missing information and even errors. The microfilm is of the original records so not perfect but better.
There is a new website which is helpful for other cemeteries belonging to the Archdiocese of New York. Calvary isn't searchable online yet but several others are.
Google Calvary Cemetery Queens for phone and address or I'll try to post the link--
https://calvaryandalliedcemeteries.com/calvary-cemetery