How do I go about adding an item to the barrel outside the Census office in Seyda Neen without overwriting whatever item is already in there that was added by another mod? I added this enchanted ring to it. Now the ring is in the barrel, but there was another item in there that I don't see anymore. Makes me wonder what other possible items are suppose to be in that barrel that have been added in by mods.

If you have two mods trying to edit the same object, the one which is loaded latest will win out (your modification). The only way that I know of to circumvent this is by merging objects.

http://www.gamesas.com/topic/1367045-smartmerger-3/ is a fairly new tool which looks promising; though I have no experience with it. You may want to investigate merging the objects from your mod with the other mod using SmartMerger.

Ooh, that's what merging objects does. I thought it only merges the stats of weapons and armors.