Ashara, both methods of what you have mentioned are the Preferred ways to change a coordinator. That is simply issue a Global network reset (ATNR1) on a local node.
The hard way is to follow the steps in the manual via the terminal emulator and manually issuing the AT commands.
Example: replace a coordinator (security disabled)
Read the OP, OI, CH, and ZS commands on the running coordinator.
Set the CE, ID, SC, and ZS parameters on the new coordinator or load coordinator firmware on the module, followed by WR command to save these parameter values.
Turn off the running coordinator.
Set the II parameter on the new coordinator to match the read OI value on the old coordinator.
Wait for the new coordinator to start (AI = 0).