RoatanMan has a good point -- you can find ways to make your honeymoon special and romantic no matter where you end up. Also, you don't mention what region you are looking to travel to, what month, what budget, what kind of diving you like, what other activities you are looking for, or what you define as being romantic. That said, based on my own taste and opinions, here are my recommendations:
In the Pacific, I second the recommendation for Hawaii (the Big Island is my favorite, but all have wonderful attributes). Also Bali, Indonesia. For our honeymoon, we spent one week on Bali and one week on a liveaboard that sailed out to Komodo. The diving week wasn't "romantic" so much (but fun!); the week on Bali was really magical. French Polynesia is of course honeymoon central -- but it also is supposed to have good diving. I haven't been there myself, but I know people who've gone and loved it. Ditto Fiji. I've also heard people wax poetic about dive honeymoons in Thailand and the Maldives. We've been to Australia (Sydney, Cairns, and the GBR) and didn't find it to be as special as Indonesia -- I'm glad we chose the latter for our honeymoon.
In the Caribbean, St. John is a pretty and romantic island, although not the most spectacular diving perhaps. I've heard really good things about Anse Chastenet and the diving on St. Lucia but haven't been there myself. Places I've been to that I may have enjoyed very much but would NOT have considered romantic enough for a honeymoon: Roatan, Bonaire, Curacao, the Riveria Maya, Cozumel, and Ambergris Caye, Belize. (Mainland Belize, however, has potential). And I'm sure there are lots more great places in the Caribbean that people can recommend.
Happy planning!