The first thing I would check is the fall away on the front end and the swing arm. It would be best to get the bike aligned before putting a stabilizer. Also, take a look at the rubber mount,see if it's getting soft or cracked somehow.

 

I just traded for a 2010 Ultra. The dealer told me the wobble that bikes had experienced over many year prior was due to the frame flexing in corners. And I had several bikes that did wobble, but this one does not. So I'm thinking he is right. I'd say a stabilizer, or a trade...