It depends what type of dancing they are looking for. For elegant dancing Crystal is probably the best. For disco and such, skies the limit as most major cruiselines from Carnvial to Royal Caribbean have lots of high energy dance venues, such as Royal Caribbean's Boleros.
Regent ships offer ballroom type dancing before and after dinner with a small band in the Horizon Lounge, although the dance floor is smallish. Longer cruises seem to attract the most dancers. For the disco-minded (that would be me), Regent offers a DJ with music in the Stars Nightclub. That one is hit or miss depending on the demographics of the particular cruise.
I would be very careful about the Regent experience. As Donna mentions it is really "hit or miss". I do like the concept, but I have heard that with the small dance floor and a demographic that seems to be less inclined to engage in classic dancing, it is hard to recommend the cruise line if that is the issue. As for its Stars Nightclub, I have never heard of it being a lively spot, but again the demographic on any particular cruise could change that.
I've been on Regent cruises where the dance floor has been packed for almost every night of the cruise. And, I've seen Stars lounge when it is filled with dancers having a good time. On any cruise, no matter the ship, that segment's demographics can make a big difference. Unfortunately, there's no way to predict it before choosing a cruise. With over 200 nights on Regent, I'm comfortable recommending them.
If people want to dance the night away, they're probably looking for a lot of venues, a variety of dance experiences. I say Carnival probably offers the best choices for late night dancing from disco to ballroom and Latin and some good old-fashioned Lindy-ing. And I would go on record that it's standard for the line, not one specific ship.
Depending on the age of the couple, I would recommend Carnival, Princess, Royal Caribbean, or Holland America. Each will provide a variety of dance choices within a variety of venues - pick out a few specific ships (within their age range) and let them choose what other features attract them to a ship besides dancing. That way you've got all the bases covered by providing them with other activities they may enjoy as well.
Happy selling and take care,
The big ships with plenty of venues and big bands would be best.
I'm an Aussie so I haven't been on Carnival, but found that Celebrity was good for that sort of dancing.
And the P&O World Cruises ships - Oriona, Aurora, etc would be excellent along the fabulous Cunard "queens" - QM2 and the soon to be launched Queen Elizabeth. I believe the Queen Elizabeth is going to offer a "golden age of cruising" type experience with tea dances and other traditional touches -- those ships have superb ballrooms.