If you actually lied and you want to correct it, that is admirable, HOWEVER if you were my client I would advise against it because you are subject to ALL of the negative outcomes listed by you in the your question. Almost for sure your child will be taken and you will have to deal with that through CPS (you should be able to remain custody because you are actually doing the right thing). Jail is almost a certainty. Perjury is a VERY BIG DEAL and so any attorney would have to advise that jail for such a case is probable for sure. Getting the court to believe you is a question mark. You would have to go through an attorney and have him/her contact the different agencies and court in order to get the ball started.
You sound very noble at this point, but disclosing your lies will risk criminal charges and further family court actions. Perhaps there is another way for you to come to terms with your past behavior.
You say your husband voluntarily stopped visits. Did DYFS close the case? If there isn't a court order prohibiting your husband visiting with the child, perhaps you can call him and offer that he slowly resume. If there aren't any issues the court will not get involved.
Please be advised my answers to questions does not constitute legal advise and you should not rely on it, due to the fact that we have never met, I have not been aprised of the facts in you case nor have I reviewed any documents.
Retain an attorney who specializes in criminal and DYFS cases. You may also need a psychological evaluation to explain the stresses that led to your misrepresentation. You will not go to jail and you won't lose your child, but joint custody sounds possible.