Some places to post a job listing for a babysitter are Craigslist and the local newspaper. Another way to market babysitting service is by word of mouth.
The appropriate category for placing a babysitting job listing on Craiglist is under the household services category. This places it with other domestic services, such as house cleaning and handyman work. Do not put personal contact information in the ad. Let potential clients make contact by way of messaging through Craigslist.
Another good place to advertise is in a local newspaper's classified ads. Although this costs money, it gets notification of the service to a large audience.