A worthy goal, I would opine...
... since full charge loads will break one's wallet and one's fool neck.
The first problem is getting suitable bullets for plinking.
Lyman lists bullet moulds for .58 caliber minie balls in weights from 315 to 566 grains. They have a .69 caliber minie weighing 730 grains, but I don't know if you could resize it enough to work. Lyman also lists a .58 caliber round ball, without specifying the weight. None of these are close to the full power load weights of the Nyati, but you did say plinking loads.
Powder charges are another matter. Were it me, I'd start with a fairly fast rifle powder and about one-third to one-half a case with a wadding to keep it in place. However -
With a short google, I found this website you might want to peruse:
http://www.reloadbench.com/cartridges/w585nyati.html
They even have 'plinking loads'.
Oh. If you need empty brass, Midway advertises it at $109.99 per box of twenty; shipping not included.