Hi, I'm Catholic and ttc and have a pretty good knowledge of what the Church does and does not allow in terms of fertility treatments, having studied theology myself and also having married my wonderful husband who was in the seminary for 4 years before he met me.

The Catholic Church does not allow any artificial reproductive technology that takes conception out of the union of husband and wife. It does not allow this not only because it separates the procreative and unitive acts of marriage, but also because those technologies almost always inevitably result in the deaths of children. In IVF, for example, 10 eggs might be fertilized (which means that from the moment of conception that did occur, a child was formed; tiny and not wholly formed, true, but it does have a soul from the moment of conception), and only 1 or 2 fertilized eggs will be used. The other embryos are either frozen or disposed of-both of which go against the dignity of the human person. Humanae Vitae is a great document about this from the Vatican.
The Church does allow things that keep the procreative and unitive aspects of marriage together and help the body to do what it was naturally made to do. I use Napro technology myself. My husband and I started trying for a baby nine months after we were married. We were successful on our fourth cycle but that pregnancy ended in miscarriage around the 8 week mark in August. I don't have any major infertility issues, but I do have low hormone levels. My Napro doctor actually had me take HcG injections after ovulation on the cycle that I conceived as it would increase progesterone levels in the second half of that cycle and estrogen levels the first half of the next cycle. Of course, we couldn't know I was pregnant when I began that treatment and I actually conceived without HcG as conception had already happened by the time I started the HcH (3 dpo).
What my doctor has had me doing now (the last two cycles) was to take a progesterone suppository from days 3-12 after ovulation and clomid from days 3-7 of the cycle. These treatments are great because they not only increase the chance of having a successful conception and pregnancy, but they also work to correct the problem at its root, rather than just try to override it. I have also heard that if clomid is going to work for someone, it is usually within the first 4 cycles, so I'm keeping my fingers crossed. I was a little impatient this time around and tested on day 10 past ovulation and about five days before I was expecting my period which is a little early. I should be getting my friend Thursday or Friday unless of course I get that bfp.

All I can say is that Napro technology actually has a higher success rate than IVF and many other ART's and it is totally in line with Church teaching and really helps the husband and wife to grown in their relationship and understanding of each other. If anyone has any other questions, I'd be more than happy to try my best to answer them!
God bless you all!