Get a diaphragm or use condoms. Barrier methods can be very effective.
If you do start charting, you could just use them until after ovulation. It might be hard to chart until your periods return after the baby though.
If you're "done", your DP could have a vasectomy. I am also at risk for clotting issues so stopped BC years ago. DH and I have used withdrawal with 100% success so far (a total of 4 years off the pill and trying to prevent pregnancy). If used correctly, you only have a 4% risk of pregnancy each year. I think we're pretty fertile because I got pregnant quickly with DS and the very first try with this baby, so I have a fair amount of confidence in the method. You could do that until you got your period back, and then start using that along with charting as well. Taking Charge of Your Fertility will help you with charting.
My doc's recommendation was the Paragard IUD because it doesn't use hormones.