Look for marriage records of the children in NJ. You did not give names so I can't check. FamilySearch has index/abstract of many Essex Co. marriage records from 1878 to about 1900. In some cases, the exact birth place may be given. If it is not given on the abstract, it may still be given on the original record, which you can get from NJ Archives for $10. Death records for children may also give exact birth place, but you'll have to have a year to get those records. If you know death dates, then you can get death certificates. However, marriage records are easier to get, so I'd start with those.
PS: I found an old query of yours and got the name of the family you are working on.
Benjamin P. Bernard, son of Jacob Bernard and Sarah Hurman, married Mary E. McGuire, 15 October 1890, East Orange, NJ.
I would send for this marriage license. If that doesn't give you the info you want, see if you can identify/locate the Catholic Church where they were married (listed on the license). The Church should have a record of where Benjamin was baptized.
There may be others of your family listed as well.