It depends on why they are anti-gun. Chances are, if they are adults, they've formed their belief and there is little likelihood of changing it unless something major happens in their life (like they become a victim)
having said that, people form opinions based on 2 things. logic and emotion.
you have to deduce what the basis of their opinion is (logic or emotion) and then target your response as appropriate.
If their opinion is based on emotion, emotion will be most effective to change their mind. If it is based on emotion, logic won't have much effect. Your logic based response will either be over-their-head or it will be discredited because it doesn't fit their pre-conceived "feeling" of how things should be.
If their opinion is based on logic, then statistics, facts, etc will be effective.
Its likely that if they are an adult and have paid attention to anything over their lifetime, if they had a logic-based conclusion, it wouldn't be anti-gun (as we all know, the facts and statistics as well as common sense completely demonstrate the efficacy of law-abiding people being armed)
People who's opinions are based on emotion don't admit it, so you have to ask probing questions. People who's opinions are based on emotion OFTEN misrepresent statistics to justify their emotional conclusion. They've probably heard something trotted out in the anti-gun media that they latched on to as fact.
A "red flag" that you are dealing with someone's emotions, not logic is if you show them documented proof, either in the form of clearly demonstrating the statistics they tried to quote you are false, or you make a common sense argument that they have no response for, and THEN their response remains something like "thats fine, but I just don't like it" or a dismissive "well, your statistics must be flawed"
If they say "hmm, I never realized that" then you have a logical thinker.
Emotional thinkers continue to deny deny deny and in the end, just mentally shut-off when they can't refute your supporting evidence.
For an emotional thinker you have to appeal to their emotions. Instead of the logic based "well according to EVEN the most conservative measure of defensive use of a gun, 200,000 times a year, a gun is used defensively which makes the incidence of accidental shootings statistically insignificant" you would want to appeal to their emotions: example - "Do you have a daughter?" if they say yes "if your daughter was walking home from working her college waitress job alone at midnight and she was being followed by a thug would you rather she had JUST a cell phone, or a cell phone AND a gun?"
Ask a mother if she were in her car with her kid in the far back seat if a thug came up and tried to car-jack her if she would just get out of the car and let the thug drive away or if she would want to have a gun to defend her innocent baby.
once you break down the emotional barrier with an anti-gun person THEN logic can be used to fortify your position, but the emotional wall must be broken down first with emotion, then once you have turned their emotions in your favor you fortify that with logic.