The 60 days extention IS available if your name is on the childs birth certificate even if you're not married or haven't been through the court process. It's only for the 1 year extention that you need to go through court.
You can get the single entry Non imm O with just your name on the childs birth cert but to get the 1 year extention you need to go through the court, proving you're the father.
Frank Edvin Johansen You can't convert the Non Imm ED visa to Non Imm O but you may be able to change the reason for your extention of stay, if you're on one, providing you meet all the requirements