From the NJT website - “Only service animals accompanying customers with disabilities or their trainers, police dogs, and small pets in carry-on travel cages are allowed on-board NJ TRANSIT trains, buses and light rail vehicles”

If it’s you’re only way home and you don’t have a carrier, guess you’re gonna have to do what you have to do. But I have seen conductors chew out passengers who did not have their dogs in the proper carriers and threaten that they have to get off at the next stop. So you’d basically be rolling the dice if it may happen to you. And you’d be asking for trouble on a crowded train so test your luck during off peak hours.