That is outright blackmail. If it is legal where you live, you need to tape record your conversations with her. You can find out if that is legal at http://www.rcfp.org/reporters-recording-guide. Once you have her on tape making threats of false accusations, then you either have the option of taking the tape to the police immediately and asking that extortion charges be filed, or you can wait until she makes the false accusations, when the police will be able to add making a false report to the extortion charges. That tape will be worth many times its weight in gold. Carry a copy with you at all times, so when the police come to pick you up, you can tell them you expected this, and ask them to listen to the tape. Make sure this is a copy. You want to keep the original in a safe place.
If it is not legal to tape record conversations where you live, then keep a journal of every contact you have with her or the child. See http://www.deltabravo.net/custody/tips1.htm for tips on keeping documentation. You will also find links to many useful resources here – http://www.deltabravo.net/.
When you do see the child, make sure you have someone else with you at ALL times. Never be alone with the child. That way, when she makes false accusations, you will be able to prove that they are false.
Your child needs you. You can bet that she is telling him that you just don’t want to see him. Her threats and using the child against you are clear signs of an abusive personality. Your child will need protection from that abuse.
See the report Family Wars, The Alienation of Children and other articles on the PAS Information Archive for more information on this type of abuse.