Here is an excerpt from a bulletin put out by the NJ Dept of Community affairs - Nj Anti Eviction Act code N.J.S.A. 2A:18-61.1(j):
"j. Tenant Continously Fails to Pay Rent or Habitually Pays Late If the tenant continuously fails to pay rent or habitually pays late, after written Notice to Cease, the landlord may file a suit for eviction. A Notice to Quit must be served on the tenant at least one month before filing a suit for eviction. Note: The Courts have ruled that habitual late payments means more than one (1) late payment following the Notice to Cease. Also the N.J. Supreme Court ruled that a landlord after giving a tenant a notice to cease late payments, must continue to give the tenant reasonable and sufficient notice when accepting further late payments, that continued late payments from the tenant would result in an eviction action. If the landlord does not give this continued notice, the original Notice to Cease given to the tenant may be considered waived by the Court."
I am not an attorney, so definitely get legal advice if you need ... but this should at least point you in the right direction.