If you are truly any credit card (not saying I'd blame you if you were) then the easiest thing is traveller's checks. Bring enough to cover the deposit minimum's that IslandCruz calls out plus some. Once you put your cash deposit down and are issued a sign and sail card, realize they will charge your "auto gratuities" the first day, so your deposit is going to be used up quickly. SO they will ask you to add more or your sign and ail card won't work until you do. It really depends on how much on board spending you plan on doing, but between drinks, pictures, spa, and excursions, you can go through $1000 for a week cruise quickly.
If you HAVE a credit card and just don't want charges on it, you can use the card for your account backing and the last night of the cruise go to the pursurers desk and pay your balance. (They will give you a final bill the last night or you can check your account on the TV in your cabin) If you pay off the balance, no charge will appear on the card.
Just food for thought....
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
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013