I had a dyfs case in 2008 that closed in 2009, I was recently offered a position working with children and it requires a background check. Will I pass

It is difficult to say because I don't know the criteria the place will be using to determine whether or not you "pass".  You should explain the situation to the employer.  If the DYFS case was opened, and then closed becuase nothing was found to be wrong, then that's not a problem.