What’s the best liability insurance coverage to cover parents from physical harm and/or incidental damages caused by their minor child?

You want a good general "umbrella" policy, which is usually bought on top of  your homeowner's  or rental insurance. If the child is at or near driving age, make sure you also have ample automobile insurance coverage. The best thing to do is to sit down with an insurance agent you trust (if  you don't know one, get a trusted recommendation) and let them know what you're worried about--the agent will help you select the right policy, limit, and deductible. Two suggestions:

1) Do not use a family member or  personal friend as the agent: if something goes wrong (e.g. they mess up coverage somehow, which is very unlikely, but can happen), you want to be able to sue.

2) You often get what you pay for: sometimes cut rate insurance is cut rate because the agent and/or insurer will not stand behind the policy and/or provides bad customer service. It's not worth jeopardizing coverage to save a few dollars per year.

For whatever it's worth, I use Chubb. I have no affiliation with them, but I recommend them because even though they are a little pricey, they have always provided good customer service and have stood behind all claims to date. Get other recommendations, too, but as I say, for whatever it's worth, I've personally had good experiences with them.