You can quickly change accounts if you're using the Facebook app on your smartphone by following the instructions below:
Launch Mayor Match first then log out of Facebook.
Launch the Facebook app.
Log out from the current account.
Sign in with the other account.
Open the game and sign in using your Facebook credentials.
Please use the methods below to access your account if you don't have the Facebook application installed on your device:
Launch Mayor Match first then log out of Facebook.
Enter your login information by tapping the Facebook login icon.
Tap the bottom right compass symbol to launch the Safari browser when the "Confirm Login" pop-up opens.
Log in to Facebook from a Safari browser.
Sign in to Facebook through Mayor Match.