Putting a limit on the credit card doesn't work since the sail and sign card charges are applied to the credit card at the end of the cruise. It does not check the limits for each purchase.
The best way is to assign their cards as cash accounts (I think the minimum is $250 per card, but since you are a family of four, you may be able to put less on them.) That way, once they spend whatever you put in the card will no longer let them charge anything until you put in more money.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013