A common rule of thumb says life insurance protects an income. Kids don't have one, so they don't need it. I'm a father of three, and I disagree.
My strongest reason is the one I understand best. We have two incomes in our house. If we lost a child, both of us would need time to grieve without worrying about going back to work. At least one income would take a hit for a significant stretch, and probably both. We have other kids who still need care. A policy on me doesn't help in that situation, so without coverage on the child we'd dip into retirement accounts or go back to work right away.
There are other reasons people give. One is guaranteed insurability. If a health problem shows up later, a policy bought when your child was young is already theirs. A diagnosis at forty can't take it away. Another is covering basic expenses like funeral costs. The coverage doesn't need to be large. It should cover household expenses and replace some of your income for a limited period.
There are three common ways to buy it. The simplest is a child rider added to your own policy, or to employer coverage. Children are covered automatically, and the cost is usually a few dollars a month. It typically covers small amounts, maybe funeral expenses, though you may be able to raise it.
The second is term insurance on the child, which is cheap. Pick one that's convertible, meaning it can later be changed into permanent insurance without a new health exam. If something disqualifying happens, you can still convert.
The third is a permanent policy, such as whole life or indexed universal life (IUL), which builds cash value. I put IULs on my own kids, funded at the maximum so we don't have to worry about the cost rising later. The reason to fund heavily is that the cost of insurance in a policy that's lightly funded tends to creep up as the insured ages, and by 65 or 70 it climbs a lot each year. With a young child the cost starts very low, so a heavily funded policy builds a lot of extra cash value. Whole life is also an option, with a 10-pay or 20-pay schedule.
A permanent policy on a child is a long commitment, and an IUL's credits depend on an index and a cap that can change. A loan against it lowers the cash value and death benefit while it's outstanding.
This was a question I took on in a video on life insurance for children. Decide how many months of lost income you'd want to cover, multiply it by your household's monthly bills, and use that as the first number you ask about.