Media outlets say Eddy's defense team also wants the trial delayed so it has more time to prepare and to conduct psychiatric evaluations. It is currently set for the week of Oct. 22.
Besides murder, Eddy is charged with kidnapping and two counts of conspiracy. Shoaf awaits sentencing.
Both are being held in juvenile detention facilities, but their cases are proceeding in adult court.
Benninger also argues Shoaf's confession should be suppressed because investigators questioned her without her attorney's knowledge or consent.
Prosecutors have said they plan to recommend a 20-year prison sentence for Shoaf and will oppose any move to have her sentenced as a juvenile. But she could get as many as 40 years under the law.
Shoaf's family issued a public apology but has made no further statements.
Eddy's family has never commented on the case.