Police say 28-year-old Shanel Nadal of Manhattan was visiting the children at the Forestdale agency in Queens on Monday when she took them.
They range in age from about 1 year old to 11 years old.
Nadal might be traveling with the children's father, 34-year-old Nephra Payne.
The couple apparently lost custody of the children in 2009, though it wasn't immediately clear why.
The South Carolina Law Enforcement Division said Friday that the Paynes have ties to the southeastern part of the state.
At the time of their abduction, the children were split up, living in three different foster homes in Queens.
Five of the boys were in Jamaica and two in Springfield Gardens. Sister Neferrti was placed in St. Albans.
Police issued an alert for a black Chevy Suburban with the license number EXZ5896.
All of the boys are named Nephra Payne.
The children have different middle names. The children range in age from 11 months to 11 years old.
A source familiar with the family says that the mother took at least one of the children out of state in May or June without permission.
They still allowed her to have the supervised visits once she returned.
ACS sources say Forestdale is well known to be lax in issues of supervision of parental visits.
Forestdale is a not-for-profit family agency based in Forest Hills, Queens.
They have four main programs - Foster Care, support for pregnant and parenting teens, family crisis intervention and a Fathering Initiative.
Anyone with information is asked to call police.