It will vary from ship to ship. I just returned from the Brilliance of the Seas sailing out of Barcelona to the Mediterranean. On this ship and itinerary, My Time Dining isn't as popular with the passengers. Given the itinerary, and passenger mix being older (which they like traditional dining) and Europeans traditionally eat later anyway. So late dining works fine for them. The My Time Dining section on the
Brilliance was only about 400 people on this cruise. MTD only used 1/2 of the upper level of the dining room. In that section there were many tables for two. I would say more tables for two than larger tables. Keep in mind this was a Mediterranean cruise with only about 35 children on the whole ship. It would make sense that a Caribbean cruise with 100's of children and more families; that they would have larger table and less tables for two. If you make an advance reservation for MTD and make it for an earlier time like 6:00, 6:15 PM or for later times 7:30, 8:00PM , then you shouldn't have a problem requesting a table for two.
Corkgirl, I would check with the cruise line on your reservation to ensure they have you listed for My Time Dining. The description and information you received sounds like information for a fixed time. Those assigned to MTD will only have "My time dining" printed on their SeaPass.