Dual Citizenship for Children

I'm sorry if this is the wrong group, but I was wondering if anyone knows the law concerning dual citizenship for children? I am wanting to apply for dual citizenship in both the us and the eu as I am eligible due to my parents being eu citizens and me being a us citizen. I would like to know if my child would automatically become a dual citizen as well when they are born or if I waited to apply after they are born if they would lose their eligibility? Thanks so much!