They were convicted in October of looting the philanthropist's fortune.
The New York Times says the appeal includes an affidavit from Judith DeMarco, who had held out for acquittal. DeMarco says a fellow juror made what she perceived to be threatening remarks and gestures.
Astor, who suffered from Alzheimer's disease, died at age 105 in 2007.
Her 85-year-old son is a former U.S. ambassador and Broadway producer.