Doubtful. The FMLA allows an employee to take up to 12 weeks of leave for the birth of a son or daughter of the employee and in order to care for such son or daughter; or for the placement of a son or daughter with the employee for adoption or foster care.
Unless this child is a foster care situation, then it does not appear the FMLA applies. You may want to contact the federal Department of Labor to discuss your specific situation, just to be sure: 202-693-4650