There's a "Subscribe to this feed" link on every public library page.

For a private group, you'll need to generate an API key from Settings.

Even if this answer would be much to late for you, michelm, others could profit from it:


Creating the feeds API key:

In Settings -- the link is on the upper right, left to the logout link -- click on feeds/API, then "Create new private key". Then you should deactive in your case everything under "Personal Library", select "Per Group Permissions" (under "Specific Groups") and then you can choose for every group you've created (?) a "Read Only" or "Read/Write" access or leave it as "None" = No access at all. At the end, click on "Save Key".


Reading/Publishing the RSS feed:

A functioning feed link would be
https://api.zotero.org/groups/GROUPNUMBER/items?key=FEED_KEY where you have to replace GROUPNUMBER with the number of your private group and FEED_KEY with the 24 characters long key you've just created. You will get the GROUPNUMBER if you open the group library (in the browser) and see at the URL behind the link "Subscribe to this feed" in the left column (below the collections and the tags).

For public group libraries you just need to click on "Subscribe to this feed". That's all.

Unfortunately there seems to be a little bug* for private group libraries which means you have to do the above manual workaround.

* @Dan: In my private libraries, the feed link links to "www." instead of "api.". Anyway, the link would not function without a feed key, right? So, it need's to be handled in another way: for example after clicking on the link, a list with all possible feed keys (which have at least a read access to this specific group library) should be shown or if there isn't one, a good notice should be shown that a feed key has to be created and so on.