What I would do here is to contact the zoning office of your particular municipality and discuss it with someone there. See if they believe that you can have any chance of getting a variance. Now, there's always the possibility of talking to someone anti gun, so the conversation could be tainted because of that, but you really have nothing to lose by trying. If there is a chance, or you want to try anyway, find out what is involved with getting one. The process may vary from place to place.
Hopefully, you don't live in a place which is "governed" by a homeowner's association, or you will have multiple problems above and beyond just municipal zoning. I could never live in any area which has one. I know people who do and what they have to go through for simple things regarding the property they bought and paid for is just ludicrous.