Missing admin_centre in relation

Theoretically, it is possible. In practice it gets a bit cumbersome or even impossible. Here's what you have to do:

1. In edit mode select the node that should become admin_centre.
2. In the left panel scroll down to the bottom and open the section "all relations".
3. Press the "plus" button underneath. You see a new empty box above.
4. Click on "select a relation" and select the relation that you want to add the admin_centre to, e.g. Ajman (3766482)
5. Add "admin_centre" in the "role" field underneath.

The problem lies in step 4. As far as I know you cannot manually add a relation there but have to select one of the entries in the drop down list. That list only includes a few entries, though. I suspect some existing member of the relation has to be visible in the editor window for the relation to show up.

For Ajman I succeeded getting the boundary in the relation list like this: I selected the node 262479959 (place=city, name=عجمان). I am guessing this is the admin_centre you want to add. I then scrolled out as much as was possible without losing the selection of the node and moved the map to the northwest so that the node was still visible in the bottom right hand corner of the editor window and the sea became visible in the top left hand corner. At that point the relation 3766482 became available for selection in the drop down list.

So, yes it is possible but would always prefer the JOSM editor over iD if I wanted to do something like this. You might want to give it a try if you can run JAVA apps.