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The first thing to find out is why are they afraid.

When I was in high-school my boyfriend shot himself in the head, yes, on purpose. He didn't kill himself, the bullet wasn't the right one for the rifle...something like that, I blocked alot of it, still don't remember alot of the specifics. It changed him though, the guy I loved basically did die. I developed a strong fear of guns, I knew in my head that it was silly, but in my heart, I hated and feared guns, didn't want them anywhere around me. A few years later in college, I had the opportunity to take marksmanship for PE, I did it....I breezed through bow and arrow, then came rifles...first day I broke out into a sweat, the officer (it was through the college ROTC) came over and asked if I was ok, I was honest and said I didn't know....he was patient, he knew from the first half of the class I probably had promise, he took his time asked once more if I wanted to drop the class (it would have been an incomplete) I said I was a Texas girl and the fear wasn't going to win, picked up the gun and shot it...I hit the paper at least, I got better later in the semester. He hugged my shoulder, said I really was a Texas girl and moved on. (yeh, I know, you can't do that anymore).
I say all that to say, the fear came from some place, but when I was ready and had the opportunity, I took control.
You have to find out, is the person afraid of guns because of an incident, or because they've been fed a load of garbage from the media and school system and have bought it all their life....if it's the latter, well, your battle is an up-hill one and you're better off praying for snow in Aug than getting into an argument with them.