That gun is the .32 Colt New Police. It dates to before the positive safety. That model was the one chosen, reportedly by Teddy Roosevelt, then New York City police commissioner, to arm the city police. Today, we would consider the .32 Colt to be inadequate for police use, but in 1896 it was state of the art, a compact, swing cylinder revolver with a decent DA trigger and, it was believed, enough power for crime fighting. Its compactness helped, since in those days police weapons were kept concealed under a long overcoat in order not to disturb the honest citizens. (It could be argued that that "see no evil" attitude toward police guns was partly resposible for the hatred of guns exhibited by present-day New York politicians and many of the state's and city's citizens.)
I think parts will be beyond scarce, as in unavailable. You could try a letter to Gun Parts Corp (www.gunpartscorp.com
has the address) as sometimes they have small amounts of parts they don't catalog, but I wouldn't hold out too much hope.