If I were you, I'd print out KRS 237.110 and when he tells you it allows the county to prohibit guns in the park, I'd hand it to him and say, "Show me where". He won't be able to do it. Then show him KRS 65.870 and tell him that the county is in violation of that statute. If he's smart he'll say it's in KRS 237.115 and then you tell him that's only for concealed weapons and in buildings. I would never lead him to 237.115, let him squirm, but be ready for him to say that. You might also tell him that prohibiting concealed carry does no good. It only causes people to uncover and OC.
KRS 65.870 can be read and printed at:
KRS 237.115 at:
KRS 237.110 at:
AGO 96-39 at:
I'd print them all out and take them with me. Good luck.