Can a verbal agreement regarding child custody override a court order?

No. Only a court order can override an existing court order. A verbal agreement will be considered by the court in rendering its decision but the verbal agreement in and of itself does not override the original court order.

There are some hurdles you have to overcome with a verbal agreement. How can you prove there was ever a verbal agreement in place. I had a verbal agreement with my ex regarding custody of our daughter. She the resided to back out of our agreement and denied ever agreeing to anything. Fortunately I had a call recording application that complied with Federal and Texas State Laws (it announces that its recording the conversation at the beginning of the conversation). Since I was able to prove that we had a verbal agreement, the court honored the verbal agreement. So, a verbal agreement may lead to a decision in your favor if you can prove that an actual "valid" verbal contract has been made