Yes, you could potentially be liable if you provide or perform any sort of "vetting" process or recommendation/referral process for the nannies or babysitters, and one of them turns out to someone who should not have been referred or passed vetting. You exposure would be much less if, like Craigslist, you merely act as an online "bulletin board" and do not touch, review, vouch for, etc. the content in any significant way. It is strongly recommended that you consult in detail with an attorney with experience in internet law before doing this.