Well, I can think of a few other items I'd do first. But, there must be some reason you're asking about a damper, so let us know. I'm at 57,500 miles on my 1200 Sport, and have found it to be as stable as a gyroscope, whether running 80-90 on the slab, or working my way through the twisties. Never a sign of instability.
Now, I will say, that the original tires left a lot to be desired. My bike took loads of counter steering pressure to enter a turn, then, abruptly, the bike would want to fall into the turn, requiring reverse counter steering to recover.
I first changed to ME880 tires, which cured the problem, but were slightly harsh.
A switch to Michelin PR3 tires front and rear was the solution to nice handling and good mileage. I may try the PR4 next.