I second Lisa's comment about capacity. They actually stop taking bookings for kids when the capacity is reached.
However, depending on the ages of your child, I would not wait til the 2nd day to register them. If they have a bit of stranger anxiety, it's good for them to get into a group at the beginning. Some kids won't join a group of kids who already "know" each other. Definitely register as early as you can. Our first cruise, DD got "lost" just before the boat drill. Since we hadn't hit the kids club yet, they had a hard time figuring out where to send her (she got the room number mixed up, 7005 became 7050 in her mind). 2nd cruise, we registered the minute they were open!