Jeannie, if you called Royal Caribbean direcly and the reservations agent told you there are no tables for 2 on the Empress, I guess he knows what he's talking about. You could try calling again and asking someone else. If that's the case, I suggest asking for a large table, so there is more of a chance of connecting with other people you like. If you end up at a table for 4 and, for some reason, don't like the other couple, just ask the maitre d' when you leave to be switched to another table for the next night.
In any case, when you get on the ship, you should go talk to the maitre d' and tell him it's a special anniversary, and ask him if arrangements can be made to have a table for 2. There may be one or two tables set aside for just that purpose.
Just as an aside, I've had the experience, as have many of my clients, of sitting at a table I didn't think I'd like, only to make lifelong friends with others sitting there. You may find that you look forward to dinner to connect with your tablemates, tell them what you did that day and hear their stories as well. Having compatible tablemates can really enhance your cruise experience.