Probably not, unless your adversary also considers the witnesses to be unreliable. Without physical evidence, the issue is who will be jury or judge believes. Good luck.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.
You may consider the witness statements to be unreliable, but the trier of fact (judge or jury) may not. Lots of cases are decided on testimony, without physical evidence.
Have you consulted with an attorney about this? You should. Contact your local bar association for a referral.