Do you know what type of glue was used? Epoxy is pretty standard for that service, so I'd assume that it was used.

Also, if you don't have an insert laying around you could put in a removable fighting butt which would have an insert with it. That's what I'd do in your case, but then I happen to have one laying around. If you just have cork rings and will be turning it from scratch, then I'd go with Steve's method.
Here's a link to some removable prefabricated fighting butts with the insert included.
http://www.jannsnetcraft.com/cork-fi...ts/280747.aspx
$7.75 plus $1.44 for the insert in case you go without the FB.

As far as matching the diameter, you can wrap the insert with masking tape to bring the diameter up to where it would fit. Then epoxy in place.