Hi and thank you for your question.
To jump right in, I have never heard of anyone needing a steering damper on a Royal Star. It concerns me that you have a wobble at 80, and frankly to me putting a steering damper on a bike that is designed to be inherently stable is putting a band aid on a problem.
I did a search and did not find anyone who made a specific steering damper kit for your bike. There are several universal adapters that could be safely installed, but unless you just want a damper on your bike, I would rather solve the problem than mask it.
If you want to go down that road of actually resolving the problem, I would need more information from you. Obviously it is going to be a very detail oriented search, as evidenced by the fact that 2 shops have not been able to resolve it.
In their model designations for their XVZ1300 Yamaha never identified anything as a 2nd Generation Royal Star. This may have been something consumers identified with but it was not an official designation. What I would need to know is exactly which model you do have then. I am going to number my questions so I can keep your answers straight.
In 2006 they had a Tour Deluxe, a Venture and a Silverado, then Midnight versions of the same 3 which were nothing more than trim packages and color.
1.) Which model do you have?
2.) How many miles are on the bike?
3.) How long in miles has the bike had this wobble?
4.) How long have you owned the bike in miles and years?
5.) What brand of tires Ft and Rr are you running now?
6.) How many miles are on the the Frt tire now?
7.) How many miles are on the Rr Tire now?
8.) What air pressures to do you run in your tires Frt and Rr now?
9.) Do you have an oversize windshield on the bike?
10.) Are there ANY modifications to the bike? (This is incredibly critical, so please list even the smallest mods)
11.) Are they any situations that seem to make the wobble more evident than other times? Such as*****conditions, carrying loads in the luggage, etc?
Let me know on those please if you want to try to resolve it. If you want to go with the steering damper the only thing I could find were generic units and universal brackets. I will keep looking just in case, but personally I favor resolving the problem.