If you're paying child support, you should have a life insurance policy that is equivalent to what the remaining support payments would be for your kids if you died today.
As a 'payor' of support, your ex is your 'creditor' according to family law. This means that if you die, your 'estate' will owe the remaining amount of child support to your ex for all the years until your kids are no longer children in the eyes of family law. If you don't have a life insurance policy for your support payments, things could get messy for those left behind, should you pass on.
Besides being recommended and often required by law, having a life insurance policy is just a good idea anyway. Most policies are term policies these days and don't cost a lot. What's more: when the kids grow up and are no longer children, you can re-designate them to be the beneficiaries of your policy. It's a little peace of mind for them and you.
Most of us want the best for our kids and this is one way that you can ensure their financial needs are taken care of even if the worst were to happen. Although it's not required that the person receiving child support (ie: your ex) have an insurance policy on their life, it might not be a bad idea for them to have one anyway with the proceeds designated for the parent who is paying support.
Child support is always about the kids and how they can have the fairest and most privileged opportunities possible despite martial breakdown. Do your best to give them the best you can.