I vote for 8x57IRS or 9.3x74R, Both are great calibers and are available in US now. Also both fit very well in 16 ga action. There is nothing wrong with WBLDon's choices( except maybe 45-70 needs 12 ga action), these are just mine. Note they are all rimmed and to quote my late brother in law" a double barrel rifle belongs to be chambered for a rimmed cartridge".
Mike