The painting is an artist's conception, apparently working without a real period revolver to go by. The "gun" incorporates features of several different makes and models.
The octagonal barrel is like an 1851 Colt Navy but the loading lever is shaped like a Remington 1858 part.
The semi-circular blade front sight differs from the Navy's simple peg.
The cylinder has 12 bolt notches which was used by the Confederate Augusta Machine Works. I think there may have been an obscure Colt variation like that but if so, it is vanishingly rare.
The contour of the rear of the cylinder is more squared off than a real Colt.
The hammer spur is more vertical than on a real gun of the type.
The grip is closer to the long swoopy 1860 type than the 1851/1873 plowhandle.
Some percussion Colts had either a brass backstrap OR a brass trigger guard, few had both parts of brass. A lot of Italian reproductions do, though.
Since the painting does not depict an actual revolver (of any make or model I know) it could not have been "Custer's gun."
There is a tradition that Custer was armed with a Webley at "Greasy Grass" but that is not proven.
http://www.gunsandammo.com/blogs/history-books/what-was-custers-last-gun/undefined
He had a sizeable personal collection and might have been seen with any of a number of sidearms at any given time.
For example, his most usual rifle was a Remington Rolling Block rather than the issue Springfield Trapdoor.