I was on the Carnival Pride last October and there were plenty of kids. I will also be sailing on Princess Sapphire this October with my 15 year old nephew and nieces age 2, 7 and 8.
I have heard that the number of kids varies not only by the time of year, but also by the itinerary and length of the cruise. Mexican and Caribbean cruises attract more families with kids than Alaskan cruises and 7-day and shorter cruises tend to have more kids than longer trips.
We always go during the school year (cheaper) and my nieces and nephew have never had a problem making friends onboard even when we did a 10-day to Alaska, so I don't think you're have a problem.
We always go in October on Carnival (last 8 yrs) , kids are 6 and 10 now and they look forward to it every year. They bring school work to do daily and enjoy the Camp Carnival with other kids. In October there are not so many kids that you feel it is a summer camp. We will be on the Caribean Princess this year (10/30/2004)and would like any news about the kids activities on this ship. Real live reviews, not just Princess info on the internet.