The solution is to buy Cowboy ammo, with a round nose flat point (RNFP) bullet. Made by many companies... Ultramax, Black Hills, HSM and others. For higher porformance (say out of a bit more modern rifle like a Marlin 1894, Hornady makes the LeveRevolution that has a soft polymer pointed tip.
Yep. Georgia Arms is my favorite. They use starline brass and good components. Cowboy action ammo is a little anemic but I wouldn’t want to be on the wrong end of it either. Hollowpoint should be OK too, Blazer makes or made an affordable version in non-reloadable aluminum. They are just plain fun to plink with. No tin can is safe around this cowboy!