I've used a cervical cap and loved it...so much better than a diaphragm... greater spontaneity and less goopy mess! Personally, I think US doctors are reluctant to prescribe it because it is more difficult to fit properly, there are limited sizes available in the US, and most women don't know about it so the demand is not very great. It's used much more widely in Europe.
I never used an IUD, but understand that they often produce heavier periods...and most are only appropriate if you've already given birth.
Those of us in the US are really deprived of some good contraceptive methods that are available in other parts of the world...especially Europe. I've heard great things about Persona, but unfortunately I don't think it is available in the US...at least it didn't use to be. There are also a variety of other methods....sponges, disposable caps, different types of male and female condoms, etc...that you might want to look into. Here is a great site that gives you some alternatives: