In consistency, common lard is probably closest to mutton tallow. It's readily available in 1 pound bricks at the supermarket. It's often commonly labeled, "Manteca" rather than lard, manteca being the Spanish word for lard.
At least, that's what I've noticed out West (Utah, Idaho and Washington).
So, I'd say that if you can't find mutton tallow, then substitute lard. If you later find mutton tallow, you can still use the lard for cooking (or dabbing behind your ears to attract Washington State University girls).
Lard is best stored in a cool, dry place. It doesn't keep as well as mutton tallow, it seems. However, once mixed with beeswax and paraffin, the resulting lubricant seems to keep a long time if stored in a cool, dry place.
Honey is antibacterial so perhaps beeswax is too, discouraging the growth of microbes that cause spoilage. I don't know.
Anyway, years ago I used to make up a lard/beeswax mix for black powder uses and it worked okay. It's not as lubricating as mutton tallow, I've learned, but the price and availability are hard to beat.
Others use a beeswax/Crisco mix. Whatever you use, don't be stingy with it. Use plenty of lubricant to keep black powder fouling soft so it's easily wiped out with a patch or felt wad, or blown out with each shot.
According to the recent book, "Gunpowder: Alchemy, Bombards and & Pyrotechnics - The History of the Explosive That Changed the World" by Jack Kelly:
When black powder is combusted, 56 percent of its bulk is left behind as solids (fouling).
The remining 44 percent produces gases that drive the projectile down the bore.
So you see, providing plenty of lubricant to keep all that fouling soft is paramount.
Not enough lubricant, and the fouling becomes hard and cakes in the bore, filling the rifling grooves and binding moving parts. Eventually, you'll have to wipe off the fouling as ample lubricant only goes so far, but using plenty of lubricant will prolong the intervals that you don't have to wipe off fouling.
