Are there any systems that can do this? I have a customer that wants to be able to change the outdial destination of an autoattendant branch quickly and easily preferably with their iPhone. They need to be able to do it remotely while on the road.

NEC SV9100. Web Browser or Possibly the MLC client with Day/Night programmed.

Most newer systems can do it with a web browser, I would think. Day/Night - does that mean toggling between 2 choices? I have a workaround for up to 7 choices using a presence app. It's not very elegant but you can change destinations in 2 seconds providing you have cellular data or wifi.