I don't know of anyone loading lead bullet ammo right off hand.  You can buy lead bullets and reload.  The first and foremost thing to determine, what size bullet do you need.  Krag bores can run from .308 to .312 and sometimes larger.  You'll need to slug the bore and see just what you have.  I use a pellet of #1 buck or a soft cast bullet for the 32 caliber pistols and a couple rods.   One rod is a stop, the other a driver to make sure the lead is fully expanded to groove diameter.

Oh, wait.  There's supposed to be a run of Cowboy Action 30-40 coming out soon.  Don't see it in stock just yet.  I can't find ballistic data either.  A 165gr RN, at usual cast velocities it would make a nice hole in a Coyote.  Hard cast, 1850fps or so would be easy to attain.  I'd want more technical data before jumping into buying them.

Something I found while digging around for you is a thing I've not tried yet.  That's coated cast bullets.  It takes away the need for gaschecks and lubes and allows higher velocities without leading up the bore. I'd buy them large and let the throat do any sizing that might be needed.  I'm still doing things the old fashioned way with gaschecks and lubes.  (You need to Login to view media files and links)

I was thinking lead just to get more spreading when it hits something as small as a coyote. Also, it would be gentle on an older barrel. Last time I had one going after a chicken I only had my 30-06 at hand and the fully jacketed round went through its chest without slowing down. Not a very quick kill.

Has anyone tried those lipstick rounds? How are the Rem rounds? This gun is an inheritance, so I want to preserve it and put big holes in coyotes. 

I am thinking the reasons Krag barrels last so long is the modest pressures and velocities. At the lower pressures the heat of the powder burning is considerably less than a 308 with the same powder capacity. It seems like a 150 grain jacketed round nose might be the best ticket for lightly constructed varmints. The round nose 150 will be a little shorter than the 220 round nose the Krag was designed for but close enough that it should feed well. Each Krag has its own preference for loads but if the barrel is near .308 in diameter I might start with this.
Before I converted my sporter to 35 caliber I had used 130 grain 30/30 flat tip bullets and I do not remember any difficulty feeding, which would be another possibility as they should expand well at the higher Krag velocities.