Brush and thong - just like the vast bulk of the Army did during the war - and 'wiping rods' - small-diameter wooden rods with a patch wrapped around the tip.
If you have 'any' manual skills at all, you can make your own.
'Very' few rifles were equipped with butt traps at that time.
For the 'Cowboy Era' - meaning the use of better rifles and 'civilization' - you need to go to the 'Public Library', and find copies of both the 'Sears, Roebuck & Co.' and 'Montgomery Ward & Co.' reprint catalogs.
They should have the full-sized ones that show better detail than the paperback-sized ones, but for your purpose, either's good.
Those are period catalogs of exactly what was available 'during that time'.
Now that said, you'll get a far cleaner weapon by using modern gear - just like GGG Grandpa did.
Vaya,
Scouts Out!