Will,
If that is a Cyrus Alger cannon, I think it was made for the civilian market, and if it's not a military gun, then it wont have an inspector's initials nor an Army or Navy registry number marked on it.
You state that it is marked "C. Alger & Co." (your quotes); is that exactly what is marked on the right trunnion face, and is anything else marked on the same trunnion face?
You also say the gun was made in the 1860's; but sixty what, and where is this date marked, is it on the left trunnion face?
Is the weight of the gun marked somewhere on the barrel?
Is there a number marked on the right rimbase end, and is this the number you're calling a serial number?
"The serial number (or at least a portion) is also present. Please forgive me, as I'm a little cautious to give that number out on the forum."
Will; I'm just curious what you think you have to be cautious about? If any of us had knowledge of this "serial number," how do you think that might end up having a negative effect on yourself, or your family?