Cathy: Forgive me if I give you info which you already have but I can't tell from your post exactly how far you are along with this family. Anyway, have you tried contacting the cemetery directly? If not, contact info is: 1401 Locust St., New Orleans, LA 70117 [504-945-9012]. Also, if you want good info on available burial records then you should visit New Orleans Public Library website at:
There are a lot of good resources but little of it is online as far as I know. Your local LDS Family Center might be able to help you with any microfilms of interest.
The Louisiana Secretary of State website has some vital records indexes online and you can order copies for a modest fee. Mr. Joseph R. Bouterie is listed in the death index so perhaps his death certificate might help, if you don't already have it.
The NO Public Library site also has the "Louisiana Biographical and Obituary" database online which you can search. If you find something of interest, then you can order a copy of the original article for a very small fee. I did a search for surname "Bouterie" and got something like 40 hits.
I searched PERSI and found an article in a local genealogical publication titled "Bouterie Marriages - Lafourche Parish".The article was published in 1972 - I can get you the citation if you wish. A copy can be ordered from the Allen County Public Library for a few dollars. If you wish further particulars, just ask.
I also found a 1894 obit for the "widow Etienne Bouterie" who died in Lafourche Parish. Survivors are not named but its fairly lenghty, given the time frame.
As you likely know, this surname, at least in the 19th and first half of the 20th century, appears mainly in the Orleans Parish and Lafourche Parish ares so I suspect that most of these folks were related in some way.
Again, don't know if any of this helps but thought I would mention it. Rick