I was born in the UK and moved to the US a few years ago to be with my husband. I'm now moving back and will be accompanied by my minor (8 months old) child. They'll be traveling on a US passport. What, if any, visa will my child need to remain in the UK with me permanently?
You were born in the UK. I assume you you are a British citizen, because you make no mention of your own visa. Because you were born in the UK, you are a British citizen "otherwise than by descent," and your child is therefore also a British citizen (by descent, however). In that case, your child obviously does not need a visa, but it will probably be simplest to apply for a UK passport for your child before you move to the UK.
Even if you do not apply for a British passport for your child, your child does not need a visa to enter the UK because of his or her British citizenship, and does not need a visa to board a plane to the UK because US citizens do not require visas to enter the UK.
(The consequence of your child being a British citizen "by descent" is that any children of your child who are born outside the UK will not be British citizens unless the other parent is a British citizen otherwise than by descent.)