A good barrel scrubbing after a few "break-in" shots (including copper removal) will often help a new rifle. With a .44, a 2" group is about as good as it's going to get, and you may have to try several ammo types to get that. 2" at 100 yards, though, qualifies as "minute of whitetail"... and if you're considering shots much over 100 yards, a .44 ain't the rifle... the energy is falling off pretty fast, and the trajectory is starting to look like a rainbow. Inside of 100 yards, it's hard to beat a short, light .44.
I shoot a 96/44, and get my best groups with a 240 grain Hornady XTP loaded just a bit under max - 1.5 to 1.75 inch 3-shot groups. Any other 240 grain jacketed softnose or hollowpoint shoots 2 to 2.5 inch groups. It shoots fair with 300 grain bullets, and lousy with 200 grain bullets.