Phil Little
"Does it exist?"
If you don't want to; "mess up the hide (pelt). For Coyote hunting."
No!
Try the Speer 130 HP or 1130 TNT, Sierra 125 SP or the Nosler 125 BT with H335 (you will not get enough Varget in the case for any decent velocity) in W-W cases with WLR primers. Start at 46 gr and work up to 49 in 1/2 gr increments looking for the usual pressure signs. 130 Speers run just under 3200 fps out of my 26" barreled M70 and shoot under MOA to 500 yards with that load.
With this cartridge (actually bullet size) you will get pelt damage, a lot of it. I have shot coyotes with FMJs (110 carbine, 147 M80 bullets and 174 gr M118 bullets) I only recovered about half of what I shot as unless the bullet hits solid bone the coyote will go a long ways before dying. Even with the ones recovered there was considerable pelt damage. SPs of 150, 165 and 180 gr still caused damage or the coyotes was lost. Choice is yours.
Larry Gibson