WHO has paid for the cruise, you or your parents? If YOU have paid for it and have the reservation number, you can go on the RCCL web page, log in and click to the reservation page itself. One of the links on there will allow you to purchase certain items to be in the cabin when they arrive, like flowers, special robes (the HEAVY DUTY robes are VERY nice), candy or wine, etc. IF your parents paid for the cruise through a travel agent, who's name you know, you may be able to contact them and they can arrainge for the flowers. OR, if you know the reservation number, you can call RCCL customer service reps (look the the number on the web page) and maybe they can help. I have posted a lot of IF'S; Dave or SOnny or Cruise Critic should be able to give you more answers, or better answers. I know that on one of our cruises, I used the reservation page and ordered two of the heavy duty robes to be in the cabin for our anniversary cruise. Good Luck, and next time, book one for yourselves also!!!
As Jim said, you will need their reservation number and cabin number. Here is a link to the cruise line's website gift shop. You can simply call RCI, order online, or download an order form and fax it.
You may not need the reservation number if you call the cruise line directly. If you know what you want to send (check gift order section of the website) and have your parents' cabin number, you may be able to place the order when speaking to a live gift order agent, using a credit card.
As Sandy stated, I don't think you'll need the reservation number. I can give you an example of what happened to me. I was sailing on the Freedom of the Seas last year. My sister sends me a text message, asking what the name of the ship was, and the sail date. I give her that information.
On embarkation day, after I get checked in, and go to my room, I see on the desk a "Happy Birthday" note from her, along with an onboard credit from her, which was her birthday gift to me. It can't hurt to have the reservation number, but what I assume happened, was my sister called Royal Caribbean, gave them the passenger information, ship name, and sailing date of the cruise to have that gift delivered. I booked directly through Royal Caribbean at the time, and not through a travel agent. I don't recall giving my sister my cabin number.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)
I called their 800 number on the website and gave them the names of the passengers, the ship name, and the sailing date to send my friends an on board credit that they could use how they wished for their honeymoon. It worked out perfectly.
We got the heavy weight robes, and truely use them mostly at home. As SonnyV said, we get the light weight robes as a perk in a Jr. Suite, but since all of our cruises so far have been in the Caribbean, we don't use them either in the cabin, or on the pool deck(too warm anyhow). They are really nothing more than heavy terry cloth, but they are nice to have where we live.