I agree with others that you shouldn't frame the argument as one in which a decrease in crime following the passage of CCW laws is necessary for the right to concealed carry to be justified.
The anti-gun argument against concealed carry is that concealed carry should not be allowed because this would cause increases in crime. In other words, the anti-gun argument requires the existence of a positive causal relationship between concealed carry of firearms and crime.
All you need to do to succeed at completely undermining this argument is present evidence that show such a causal relationship does not exist or that, if it does, it is one in which crime rates decreased in the presence of new concealed carry laws.
Example:
http://www.concealedcampus.org/pdf/ccw_gun_facts.pdf
"Fact: After passing their concealed carry law, Florida's homicide rate fell from 36% above the
national average to 4% below, and remains below the national average (as of the last reporting
period, 2005).152"
"Fact: Deaths and injuries from mass
public shootings fall dramatically after
right-to-carry concealed handgun laws
are enacted. Between 1977 and 1995157,
the average death rate from mass
shootings plummeted by up to 91% after
such laws went into effect, and injuries
dropped by over 80%.158
153"
etc.
The knee jerk reaction to such stats by anti-gun liberals is to deny that the observed reductions in crime/violence is/was due to factors other than the possession of firearms. This is fine, as it still demonstrates the absence of the expected increases in crime/violence following concealed carry laws, which would have to be observed if their positive causal relationship was correct.