Seansean, I always just shot them in the chest or mid body with 40 grain hollow points.
Very little pelt damage which was important in those days.
In the best year I ever had the pelts averaged $90 each at the Winnemucca fur buyers, so I didn't want to damage them.
I was able to buy a 3 year old Toyota Land Cruiser with the money I earned in only 5 months with bobcat and coyote fur. That year I used mostly the 222 Remington for my "fur rifle" however, but I did kill about 30 of them with my 22 mag. It was a tubular magazine fed Marlin.
I sold the Marlin the next year because in those days I could load 222Rem cheaply. And the SAKO 222 has much better range and was about 3X as accurate.
Winchester 50 grain bullets cost $22.00 a thousand then, and primers were about $.98 a flat. H322 powder was $6.50 a pound. Those 50 grain Winchester bullets always went clear through but only left exit holes about 1" across. I could easily sew them shut.
The 22WMR often didn't leave an exit at all, and if it did the hole was only 1/2" across, but I could easily kill coyotes at 300 yards with the SAKO and that was out of range with the rimrife unless I got REAL lucky.
Cheep ammo and expensive hides.
Man............I miss those days.