For a starting point, the .30-40 Krag with pressures around 40,000 psi uses 34gr of IMR 3031 behind a 200gr soft point for about 2100fps ( in a 30" barrel )
The data for the 8x57J that I found looks hot, based no doubt on the assumption that the rifle would be on a M98 action. Factory loads with a 196gr bullet are listed at 2400fps, which suggests pressures higher than 'medium'.
Another round with about the same capacity is the 8x56 Mannlicher-Schoenauer, which uses 40gr of 3031 behind a 200gr SP for 2050fps. I'd guess that would be your top end, and would certainly be an effective white-tail load at realistic range. Unless your local deer are the Kevlar armored mutants that need a .300 WinMag, as some hunters suggest...