I've never used coon grease but it is an animal fat and should work okay. But, as has been said, it is subject to going rancid. There may be some kind of additive you can put in it to preserve it but I don't know what it might be. I'd say that if you give it a try and find that it works for you, you should then divide it into small portions, enough for one day of shooting and then freeze it to keep it from going rancid.
Nit Wit suggested adding bees wax to it to thicken it and that is a good idea, too. Just add whatever amount of bees wax you need to make a lube that is stiff enough for the ambient temperature. More wax in the summer and less in the winter.
I like to melt my grease and before it cools add about a tablespoon of Murphy's Oil Soap to a couple cups of melted grease and bees wax mixture. As the grease cools, whip in the Murphy's with a fork to form a nice smooth creamy lube. The Murphy's not only makes a nice smooth lube, it also keeps the fouling in your bore soft so you can wipe it out more easily. Who knows, it may also help preserve the grease. I ain't sayin' it will, just that it may help preserve it and keep it from going rancid.