Get a balcony (at least) for maximum romance. Cruising has all the elements of romance just waiting for you to unleash. Don't be shy about talking to the cruise line coordinator to see how they can help you take it to the next level. Flowers in the room? No problem. Chilled bottle of wine? Ditto. Romantic balcony dinner for two? They can help!
I think Celebrity's ships, with fewer children, are very romantic! As ABLISS said, definitely get a balcony. We love to have room service coffee on the balcony in the morning, and also love to sit out and look at the stars late at night.
Royal Caribbean has a 4 night (Mon-Fri) cruise out of Miami that goes to Nassau, Bahamas and their private island in the Bahamas. Hubby and I are taking this cruise in Sept. Very good deals going on right now--Buy one and get the second passenger for 50% off. If you go when the kids are in school, you won't have too many onboard and should be pretty romantic.