We have a very hard time doing that, as it requires consent of ⅔ of the 50 states. If we hold a constitutional convention, it's possible that some will try to change other parts of the Constitution and at this time in US History, it could be exceedingly dangerous (and result in the 2nd Amendment being strengthened or at least left in place, but some other thing - such as an Anti-abortion amendment could result).
While most Americans would not be in favor of an anti-abortion amendment and might be in favor of eliminating the 2nd, it's not up to the total view point. California, with 12% of the US population, and NY (about 3% of the population, I think) would almost certainly be in favor of 2nd Amendment modifications, but they would weigh no more heavily in the vote than Wyoming, which has only 568,000 people. California has 39,000,000 people. Montana would get equal weight too, with only 1 million. Red (gun loving) states probably out number the others.
It's a serious issue with almost no fix at this point in time. We rely upon our Senate and our House of Representatives to make laws (and the 2nd Amendment does not say "Hey, everyone should have guns everywhere and no one should have any limits on type of number of guns!)
Indeed, it says something very different:
Second Amendment Right to Bear Arms
- A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.
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Note that the amendment itself mentions two things (a militia and regulation). So we have the right to own weapons, but it's because we needed a citizen militia/army back when the document was written and it does mention regulation - which is the job of Congress.
IMO. The solution is gun regulation, allowed by the Constitution. At least right now, that's the solution. But the gun lobby is enormous and owns so many of our legislators, IMO.