There used to be a whole bunch of small surface lots around JSQ, but in the last year or two many of those have become construction sites. Here are some good current options:
+ parking deck @ the PATH station, run by LAZ. Entrance is at the intersection of Summit Ave & Magnolia Ave.
https://www.lazparking.com/local/jersey-city-nj/journal-square---path-garage

+ 2 Journal Square Plaza aka 2940 Kenndy Blvd, just northwest of the PATH station. Enter from Kenndy Blvd southbound
https://en.parkopedia.com/parking/garage/2_journal_square_plaza_garage/07306/jersey_city/?arriving=202211281730&leaving=202211281930

+ State Square garage. Enter from Kennedy Blvd or Sip Ave
https://lots.impark.com/imp?utm_source=google&utm_medium=maps&utm_content=0730014&utm_campaign=local_us#details=73,14

+ Square Ramp, behind the Loews Theater… enter via Magnolia Ave / Tonnelle Ave
https://squareramp.com/