Carnival sells a birthday package as a bon voyage gift on its web site, that is nice but essentially just some birthday streamers and a balloon.
Your TA can arrange for a birthday cake in the dining room -- every night of your cruise, you'll hear "Happy Annivversery to You," Happy Honneemoon to You" and "Happy Byrthdae to You" sung by the waiters at tables all around you. Your own table may have more than one special event!! (The singing drives my husband crazy, but I really enjoy it.) If you decide to have your TA arrange for a birthday cake, I suggest that you mention it to your waiter privately to confirm the arrangements. On our 15th anniversary cruise in Alaska (we had arranged to renew our vows in the Russian Orthodox church in Sitka), we were very disappointed that the dining room forgot the anniversary celebration that our TA had supposedly ordered. Now I remind the dining room before the event, so that I'm never disappointed again.
On our last cruise, we purchased a special chocolate decadance cake from the tux/specialty store on Sensation for a birtthday. I brought my own birthday streamers and tape, and decorated the room and door when the birthday boy was out. The cake was not delivered when I had arranged for it, and I ended up calling twice to find out where it was. The cake WAS very good, but our family couldn't finish it. We put the remainder outside the cabin door for room service pick-up. As people went by they were breaking off pieces of it and eating it in the hallll!!! Although the special cake was nice, it was overkill -- there are so many other great deserts and food on board, that I don't think I'd ever order a cake for the room again.