The problem with insuring a car that is not in your name is that you will have to be able to show an insurable interest in the car. Typically, the owner has an insurable interest because they have something to lose if the car is totaled, while someone who is not on the registration does not. If you can prove an insurable interest, you can insure the vehicle, but that may a difficult feat to achieve.
Most insurance companies will want you to be named as a driver on the car rather than the owner of it. The insurance will still be written for the owner of the vehicle, but you can pay the premiums and be covered if something goes wrong.
Even if the car is in your child's name, you will have a hard time showing an insurable interest. In this case, an insurance agent will advise you to get a new registration which includes both you and your child as the registered owner. This same tactic will work for someone who is not related to you, but the DMV may be concerned that the car is owned by two different and related people, especially if you live at different addresses.
You can always pay the insurance for the vehicle, even if you are not listed as driver. In this case, your payment will not benefit you in any way, because you are simply acting as financial benefactor, not as someone who has anything invested in the vehicle. This method works, but introduces other problems if something changes in your relationship with the car owner. To protect your own use of the car, you should be listed as a driver of the car even if you only use it on rare occasions.