How do I protect myself from being sued if one of my neighbor's children gets hurt on my property?

You really cannot "protect" yourself from being sued.  However, if a claim is made against you, you need to notify your homeowners insurance as soon as possible.  They will hire an attoney to defend you.  In the meantime, avoid discussing the incident with your neighbor (or anyone else for that matter).  If the matter comes up, just make general statements and then change the subject.  Do not give any sort or written or recorded statement to your neighbor or anyone associated with their side of the case.  Do not post anything on Facebook, Twitter, emails, or anyhting else that can come back to haunt you in case a suit is filed.