Susie - I was able to find one more article about the cemetery. It's from May 16 1904 and includes a photo. I was amazed to see monuments; from the other article I was expecting a few dilapidated headstones.
The Jersey Journal on genealogybank is only available up to 1922. The last mention of the church is Dec 1922 - a Christmas pageant. I haven't found any mention of what happened to the graves.
I also saw a blurb on another website that claims the Mt Carmel Baptist Church took over the church site on Ocean and Linden in 1969.
There are some early 1900 google books that mention the Linden ME Church in reports from the Newark Conference of the Methodist Church but no mention of the cemetery that I could see.
You might want to contact the NJ Room at the Jersey City Public Library to see if they have anything that can help. And consider posting a query in the Hudson County NJ forum - someone monitoring it may have more info for you.
I'd love to hear what eventually happened to those graves if you ever find out.