We were on the Mariner in April of this year, and had an 8-year old boy who joined in on the kids club activities a few times over the course of the trip.
They have daily and nightly events planned for each age group- some examples of the day activities were scavenger hunts, parades, art projects, and water play activities; some night events were a movie night, a disco party, etc. In addition, they offer "free play" in the kids club room and they organize games, have computers available, etc.
You can go ahead and sign up your children for the appropriate age group when you board (our kids club registration was from 4-6pm on the day we set sail, for example). Then, when your child is interested in attending, you can bring them by the appropriate room.
There are certain hours that the kids club is open, specifically on days you're in port, so be sure to check the schedule for the day. A calendar of events/times for the right age group your children are in will be delivered to your stateroom each day.
Keep in mind, after 10pm, there is a $5 per child, per hour charge for the kids club. I believe they're open till 1am.