Does a local ordinance supersede a state constitutional right?

The answer to your first question is no, a constitutional provision trumps a local ordinance.  The answer to the second is maybe.  Does the Constitution specifically provide the right to hunt with a gun or bow?  Does the local ordinance prohibit all use of a gun or bow?  Does it allow it, for example, in uninhabited areas?  Localities do have a right to regulate even constittutionally protected activities in reasonable ways.  For example,you have a constitutionally protected right to freedome of speech, but that doesn't mean that a town can't prohibit the use of a bullhorn at 2 A.M.