We were on Mariner (RCCI) during one of the busiest spring break weeks (mid-March). There were over a thousand children on board (under 18) and they were no problem at all. We barely noticed them.
Go with a 7-night or longer cruise. Most college kids can't afford them. It often seems to be easier to handle the 7-year olds than the staggeringly drunk 19-year olds.