This website is free and allows you to either advertise a need or look for someone to fill that need.
They make their money by offering inexpensive background checks and by having people who advertise themselves to upgrade to a better profile...but I haven't needed to do this.
I would advertise your need for a babysitter/nanny and be very specific of what it is you are looking for. The website will text message those interested in such jobs and you will get responses fairly quickly. I would only interview someone who has a background check and has references.
Hope this helps!