Is it possible that anyone could make a plugin that automatically made a database backup?
You mean other than the backup task that comes with MyBB...??
I mean like it could do it automatically once each day.
Instead of that I need to do it manually.
Yes, MyBB comes with a task that backs up your database, automatically. Set it to run daily, when someone visits your board, if the task is due to run, it'll run, and backup the database.