I do not suggest any bullet weight lighter than 240 grains for .44 Specials or Mags.
However, I have been playing with this JHP Speer makes specfically for the Special. Loaded to 850 fps, it penetrates 14" of soaked phonebooks and weight retention is in the high 90's percent. It anchors groundhogs well with minimal damage. This may be the exception to my advice for deer huunting with the Special. I'm going to try it on some larger game if possible.