How to disable Facebook Messenger vibration on iOS 12
To disable vibration in Facebook Messenger on iOS 12, open the app the tap your profile icon in the upper left hand corner. 

This will open your "Me" page. You'll see the fourth option, notifications. Tapping on it will open the notifications page. You can then select the option "Notifications in Messenger." 

That will then open a page where you can toggle sound and vibration for notifications.