I would have posted this link: http://www.davekopel.com/religion/catholic-second-amendment.pdf in the comments, which were closed when I found the post below.

Catholics, The 2nd Amendment, & Subsidiarity « The American Catholic.

To my knowledge, there has been no in-depth discussion of the source and exercise of the right to bear arms in the context of CST. However there are some precedents to work from. Although the Catholic Church long lived in tacit agreement with feudal systems of government in which property ownership was to a great extent seen a springing from the will of an aristocratic class, in the last 150 years (explicitly in Rerum Novarum and subsequent CST encyclicals) the Church has developed and understanding of economics and property rights in which individual ownership of the means to provide for oneself is a natural human right. Given that defending oneself is also a natural human right, it would not seem unreasonable to assume that owning the tools necessary to exercise the right to self defense is also a natural human right, rather than something held only by rulers and those designated by them.