Dear L.,
I decided against IUDs because a girlfriend had hers taken out after the strings were hurting her husband - and if you look online, this is a common problem! I've had a few friends get pregnant while using the Nuva Ring and I wouldn't recommend it.
I, too, cannot be on the pill for health reasons.
BUT... what you can do is become very in tune with your body and learn when you are fertile. You can choose to abstain, use a barrier method, or climax by other means during the fertile times - but this is only a few days out of the month.
An awesome book to teach you about the Fertility Awareness Method is Taking Charge of Your Fertility: The Definitive Guide to Natural Birth Control, Pregnancy Achievement, and Reproductive Health by Toni Weschler . Toni has created computer program to help you track your fertility signs that is easy to use and very accurate. More information about this can be found at http://www.ovusoft.com/ .
I am not Catholic, but I have also found the information at the Couple to Couple League on this topic to be very helpful: http://www.ccli.org/
Hope this helps!
SJA
PS: From my profile, you may see the I have five children - don't be alarmed, it's not because of the Fertility Awareness Method, but rather from personal choice :) FAM has helped me to space my latter pregnancies so that I'm not pregnant and trying to care for a newborn at the same time!! (Been there!)