Personally...............
When you're trying to kill an animal (especially not for food), it probably isn't ethical to even consider a "minimum load". The point is to kill, and kill quickly & humanely.

For reference, my son took a 135lb boar using a 180gr conical with 30gr 3fg Goex with my 1858Rem. It hit him REAL hard, but still took about a minute or so for him to quit wiggling. THAT is a Max load for that gun - ok for hunting....................but not something that should be done all the time.

Since a Coyote isn't nowhere near as thick as a hog, I'd think round ball would get the job done with 27 to 30 gr of 3fg Black or Pyro P or 25 to 27gr of 3fg Triple Seven powder. Those are 90 to 100% loads in my 1858 - but it likes those loads as accuracy starts going away quickly with less powder....... as does impact energy.

BTW I REALLY like the Triple Seven 3fg.................shoots REALLY clean and accurate.....................fired off 3 cylinders worth a few weeks ago and you could hardly tell the gun had been fired. PLUS it won me a Postal match while doing it!