Most evenings this is the dress code:
Cruise Casual Dining Dress Code: Gentlemen - Sport slacks, khakis, jeans (no cut-offs), dress shorts (long), collared sport shirts; Ladies - Casual dresses, casual skirts or pants and blouses, summer dresses, Capri pants, dress shorts, jeans (no cut-offs). Not permitted in the dining room during the Cruise Casual dinner for ladies and gentlemen: gym shorts, basketball shorts, beach flip-flops, bathing suit attire, cut-off jeans, and sleeveless shirts for men.
On ONE or TWO evenings of your cruise:
Cruise Elegant Dining Dress Code: Gentlemen - Dress slacks, dress shirts. We also suggest a sport coat. If you wish to wear suits and ties or tuxedos, by all means we invite you to do so. Ladies - Cocktail dresses, pantsuits, elegant skirts and blouses; if you‘d like to show off your evening gowns, that's great too! Not permitted in the dining room during the Cruise Elegant dinner for ladies and gentlemen: shorts, T-shirts, beach flip-flops, bathing suit attire, jeans, cut-off jeans, sleeveless shirts for men, sportswear, and baseball hats.
Hope that helps. You can read the FAQ regarding dress here:
http://www.carnival.com/CMS/FAQs/Dress_Attire.aspx
Also, if you do not want to 'dress up' for dinner, there are many other places on the ship to dine. Great food no matter where you eat. On formal or cruise elegant evenings, a short cocktail dress would be great and don't be afraid to just bring the one cocktail dress and wear it both formal evenings, as there are no fashion police LOL
My rule of thumb is to dress like you would for a wedding, funeral, job interview etc. It does not have to be a $900 formal ball gown, just a nice cocktail dress or even a pant suit that you would be comfortable in.
Enjoy your cruise!