Clipper is one of those small coastal vessels and it was wonderful. While it has no rules against kids, per se, there is nothing set up for them, no kids programs, no kids playrooms. Only 2 public rooms on the entire ship (Nantucket Clipper). Still, it was one of the finest cruises of my life.
We have sailed on the following cruises:
Splendour of the Seas 10 day Jan. 1998
Horizon 11 day Jan. 1999
Paradise (2x7 day) Jan. 2000
Imagination (5 day) Jan. 2000
Dawn Princess (2x7 days) Jan. 2001
The Carnival ships had the most children, which was still not that many, and they were surprisingly well-behaved. Splendour, Horizon and Dawn Princess had maybe 10 children on each sailing. From what I understand, the shorter cruises from convenient (cheaper family travel) Florida ports have more kids aboard. Also, if you cruise over a holiday, spring break, or summer vacation, you can expect to be over-run by ankle-biters. Longer cruises have more elderly passengers and less children. Our favourites were Dawn and Splendour.