"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"
Since airguns existed at the time, it would seem logical on the surface. Unfortunately, not many people (or even the Federal Government) consider an airgun as a firearm as well as their protection being covered under the second ammendment.
So far, no-one has taken it to the Supreme Court (or needed to) for a ruling as to tthem falling under the second ammendment that I'm aware of.