You can get your name changed on the birth cert with just your name change court order, but as for mother/father switching, I'm not sure. If you're the only parent listed, I don't see why it would be a problem, but you know how weird the government can be

The best way to find out is to call the Vital Records in your child's birth state.
More than likely you can get your position changed, but you
may need to go to court a second time (and you would need an attorney for this). If you ever do a step-parent/second-parent adoption, you can dictate who goes where on the new birth certificate.
It should go without saying that if there is a second parent listed on the certificate (living or dead), that you probably cannot change your position. Take heart that many same-sex parents get stuck being listed with the wrong title too. People don't pay attention to that part anyway, and they'd probably just assume it was a mess up on the part of the file clerks if they did notice it.
Also, don't forget that you will need to change your name with
Social Security for your child's record as well. Good luck! =)