Howdy
You can find light loads for 45 Colt in the 'cowboy loads' section of most reloading handbooks. Traditionally, 45 Colt was of course loaded with Black Powder and a 250 grain bullet.
Alliant Powder has specific 'cowboy loads' listed on their website. Hodgdon does not have 'cowboy loads' listed, but if you go to their data section you can use their starting loads for nice light loads.
Many Cowboy Action Shooters use loads below the recommended starting loads for extra light recoil. This is not a good practice, the 45 Colt case has a lot of air space in it when loaded with Smokeless powders. Going below the recommended starting loads can lead to spotty ignition and incomplete burning of the powder. In a rifle, starting loads will have a very mild recoil. Loading 45 Colt is of course more expensive than loading 38 Special because the brass is more expensive and you are usually using a heavier bullet than with 38 Special. But it is still much less expensive than buying factory ammo.
You should be aware that with light loads you will probably get sooty cases because not enough pressure will be developed to seal the case in the chamber and some gas will blow by the case. This is not a big deal even though some think it is. Just clean off the soot when you polish your brass. Upping bullet weight and powder charge will expand the case and seal the chamber better.
I won a Rossi replica Winchester Model 1892 like the one pictured as a door prize at a big Cowboy match a few years ago. Nice rifle, but a little bit stiff. It would have benefited from an action job. I never fired it, I sold it and used the money as a down payment towards an Uberti 1860 Henry.
By the way, the 1892 action is very strong. You can load up 45 Colt right to SAAMI Max pressures with that rifle and it will have a lot of punch. I do not recommend going above SAAMI Max pressure.
P.S. The rifle in the photo has a curved crescent style butt plate. A carbine will have a flatter butt plate. The proper way to fire a rifle with a crescent butt plate is to hike it out a little bit farther on your shoulder than most of us are used to. If you place those sharp points against the meaty part of your shoulder, it may hurt a little bit, depending on how hot the loads are. Many CAS shooters wind up putting a leather butt pad over the butt plate to cushion the recoil. But if you hike the rifle out a little bit farther on your shoulder, so that the points of the crescent encircle your shoulder joint, it will not hurt at all, and the shape will keep the rifle from sliding up or down.
Here is a photo of a Winchester Model 1892 rifle at top and carbine at the bottom. The rifle was made in 1894, the carbine in 1916. Notice the difference in the shapes of the butt plates. These rifles are chambered for 44-40 because rifles were never chambered for 45 Colt until very recently.
. I wouldn't hesitate for a second buying that rifle. I have the same rifle in .44 and it is my favorite firearm to shoot.