I know that Carnival has a couple of CTN's in June & July leaving out of NYC... The June cruise is on Carnival Victory, and the July is on Carnvial Legend... I don't know the exact date, but you should be able to find out more on Carnival's website.
I was on CCL's website a few days ago and looking at the iten for Victory, she definately has some CTN. Just select the individual ship and you can see the iten. Click on that and you will find the dates available.