Barnes makes a bullet in .310 specifically for the 7.62x39. If you don't load your own, Doubletap Ammo loads them. There may be other ammo brands that carry that bullet and cal as well. Or you could use the lead-free ammo or bullets from Barnes, Nosler, or Hornady in 30-30, and there are others as well.
My choice would be a 223 loaded stiffly and shooting a Barnes TTSX or E-Tip. 223's are hell on deer. If you haven't seen it, you wouldn't believe it.
