State censuses were taken in New Jersey every ten years, between the dates of the federal census, from 1855 until 1915. It is currently available on microfilm from the familysearch catalog, at the archives in Trenton and at the New York Public Library, among other locations.
I have images of a few pages I have retrieved from microfilm. I will be happy to share off-board if anyone had family in Harrison in 1915, around Sixth Street, Seventh Street or Central Avenue. The images are too large to attach here.
One of the very helpful items included in that census is the name of the school attended by any children in the household - even parochial schools. This information can be very useful to confirm if you have found the correct family or if you don't know what religion your target family practiced. This census also included the month and year of birth, along with the age of each person - a great cross-reference comparison to the 1900 US census.
This census is also a current indexing project on familysearch. The images will not be available to the general public on familysearch, just an index, similar to the index for the 1885 and 1905 New Jersey Census.