Unfortunately not, because an affidavit is not a communication to the public, which forms one of the elements in the tort of defamation.
If a party is found to have lied in an affidavit, however, they may be found in contempt of court, but I think you're in a family law matter, is that correct? If so, the procedure is less adversarial, which means some of the rules of evidence are more lax. It's unlikely a family court will hold a person in contempt if found to have lied in an affidavit, however it will be - for lack of a better word - 'punished' in other ways.
Basically, family court determines cases based on which of the parties is a more credible witness. If a party is found to have lied, they will be the less credible witness, meaning the court will be less likely to believe their story and more likely to rule in favour of the other party.
Thus, rather than seeking remedy for the derogatory statements made against you in an affidavit for a family law matter, it would be better to consider how to disprove those statements to the court, either with evidence or under cross-examination. Remember not to fall into the trap of turning your case into a mud-slinging match against your ex, as well - the court wants to see both parties supporting the child's relationship with the other party, even if the other party is kind of a deadbeat.
Hope this helps.
