I wholeheartedly recommend any .44 mag load with the Hornady 240 gr XTP bullet. While I haven't shot any deer with my Redhawk (yet) I have used this bullet on four deer with my muzzleloader (using a sabot) with great success. The 180 grain would probably work just fine, but the 240 grain would be more likely ensure complete penetration, resulting in a better blood trail. The 240 grain XTP failed to exit on tne deer I shot quartering toward me. The bullet entered the left front shoulder and ended up lodged against the rear hip. It traveled through a lot of deer to get there. Oh, and there was almost no blood trail, though he didn't get far. The bullet retained 83% of it's weight and expanded to .64 caliber. This was at 40 yards, with an impact velocity of about 1500 fps.
In short, you can't go wrong with any of the new 240 grain hp designs on the market. Trajectory is not really an issue with a .44 mag revolver, so why not go with the heavier bullet, as long as the recoil is tolerable to you?