There are a variety of online resources available for Trenton research.
New Jersey Digitized Historic Newspapers (Mercer County)
City of Trenton
Division of Vital Statistics (birth, death, marriage certificates)
Trenton Genealogy Resources (Trenton Historical Society)
Birth records from May 1, 1848 to May 31, 1878. Note: more than half of all births during this time period were not recorded. For an indirect reference to these births, it is necessary to search the census records.
Death records from May 1, 1848 to May 31, 1878
Marriage records from May 1, 1848 to May 31, 1878
The 1890 United States census was destroyed due to water damage caused by a fire in the federal building where it was being held. The only 1890 census left is the special Civil War veterans’ schedule.
Some of these websites require a paid subscription but may offer a free trial