there's unfortunately no one cruise line in which you can avoid all the youngens. That said, there are far better options than Carnival, both in terms of quality and company. What you need to consider is where you want to go and the size of ship you want to be on.
Most families (with Spring Break kids) or college kids on Spring Break are going to be spending the week in the Caribbean, probably on the larger boats. Your best bet, if you can afford it, is another cruise line like Princess, HAL, Norweigan, Costa, etc. that tend to cater to the older (read: post-college) crowds. That said, if you're taking a Caribbean cruise on a 3,000 person ship leaving from Ft Lauderdale, you're going to be overwhelmed with Spring Break people regardless of the cruise line.
I would consider something like Panama Canal, the Southern Caribbean, Europe, etc. rather than one of the straight up Western or Eastern Caribbean cruises. Really, more info is needed from you to make this any more than a guessing game.