A “quoin” is that
usually-unnecessary decorative [ed.: and often structural; see comment below] stonework you see on the corner-edges of buildings. Did you know that? I didn’t. Now you can sound knowledgeable when you’re out with friends. You’ll be all “Oh hey, check out the quoining on that building!” and your friends will be like “wtf?” and you’ll explain, and they’ll be like “wow, you are so cool!” and you’ll be like “yeah, I know.” Try it! It works. Scout’s honor.
Otherwise, all I can tell you is that Madison’s Borough Hall was dedicated in 1935. I didn’t check the cornerstone (the actual cornerstone, not the quoining), but I’m guessing construction started sometime after 1930.