Was on Carnival Cruise when we played the Eagles. Found a little bar and sit there and watched the game with a bunch of Who Dats. Fun-Fun. Don't know if they carry all the Saints games, but they did have it that day. I had been a nervous wreck, wondering, from Thursday til that noon day Sunday. Enjoy your cruise.
I have run into this problem a few times. In fact, i was on a cruise during the Rams vs Saints playoff game(HAKIM DROPPED THE BALL!) Anyway, you need to be demanding and not take no for an answer. They can get any game, you just need to be persistent and bug the crap out of them. If you must, go speak with the cruise director personally.
I promise you, they can get it. I have done it at least 3 different times.
My husband won a cruise when the Saints played Bucs at the dome. We had to watch another NFL game (can't remember who was playing) and had to keep up with the Saints on the ticker at the bottom of the screen. It was when Reggie scored on the punt return. It was complete agony waiting for Saints updates, but at least we got keep tabs. You'll probably get the same.