I used the mini pill (or Progestin-only pill, POP, etc.) while nursing both of my children (almost a year with the first, over a year with the second). It is the only hormonal birth control that does not interfere with milk production as a side-effect and is safe while nursing. You do have to remember to take it at the same time every day to be most effective. There is one (can't think of the name) IUD that is non-hormonal, and I'm sure your OB/GYN can give you more specific information on different birth control options. Good luck!
Oh, and on a side-note, I cannot ever remember to take pills daily, let alone at the same time every day. Since I finally have a cell phone, I programmed an alarm for just after I get home from work every day and that has really helped me stop missing my pills! :)