How long do you have to petition the courts to appeal the overturn rights being taken and adopting your child out?

The DCS in my state remove children from parents that want their child and leave children with parents that don't want their child. Any one who knows me knows that I am a wonderful mother, my sons were my everything. I feel that the system cheated me over some one else's actions. The truth is my heart tells me that the foster parents feel in love with my son and one is a lawyer and the other a nurse. I felt like I had no chance the day they asked me to adopt my sons out. I asked the foster parents if I agree to do so would they agree on an open adoption without any hesitation they refused so I wouldn't complete the adoption papers. I really feel like the state kidnapped my sons and there wasn't anything I could do about but try to cope with it. Please let me know if there is still something I can do. Thank you.