I wonder how many making suggestions for use on coyotes or bobcats have actually got more than one or two data points.
This question comes up all the time on every forum. I have killed a couple hundred coyotes, 55gr vmax is my bullet of choice. I have tried many others, and killed enough with each to determine unsuitability for truly saving fur. I am not talking about getting a coyote tanned to throw over the couch, I am talking about selling fur year after year. I have not killed that many bobcats, probably only a dozen or so. Their skin is thinner than a coyote, an average one is about 2/3 the size of an average coyote.
I even tried (decades ago) the heavily constructed bullet to pencil in and through. It may work now and then, but is not a reliable way to get a quick kill or a save a hide.
Coyotes: I run 55gr vmax at 3050, front on shots have only a 22 caliber entrance which you can go through when you split the hide unless you are casing them. Broadside shots give the same entrance and almost never exit, I've only ever had one exit, that was at 35 yards. Kills from 35 yards to just over 600. Most in the 200 range.
Bobcats: 223's are pretty hard on them. A perfectly centered front on shot usually results in a near perfect hide. But if the shot is offset at all or angled slightly it usually blows out the far side pretty bad.
I asked my taxidermist what he shot bobcats with. Whatever he has with him was the answer. If I were going out specifically for bobcats, I would take a 17. Like the 17 hornet or 17 Mach IV.