In historic Lincoln NM, there is a Museum, and it has Some of his guns I think,, they also have some spurs that he gave to Miguel Otero, the Governor who wrote the book "The Real Billy the Kid". They also have some of the letters he wrote, and a tree stump that may have his name carved on it. It was a cool Museum. Then you could walk down the road and see the site where Alexander McSween's home was, and the Lincoln Courthouse where Billy was held. That is also a cool museum.
According to one book I read, He may have used a Colt Thunderer. Another book said the Colt Lightening. I also learned he may have used a gun called the Colt Frontier.