It should not be that difficult to set this up yourself. We did. It amounted to setting up either a sole proprietor/business for an EIN, keeping track of FICA (documenting the employer and employee side), and then paying in both to quarterly or annual taxes. We also had to file and pay unemployment taxes to our state. Not bad at all especially if you already know the nanny-to-be.
FWIW: When I shopped around, I looked into care.com. Then, the mustachian in me realized I should try it on my own.