Rifles can be significantly suppressed, but not the typical rifle. Given F=MxVxV, the mass of the bullet must be signficantly increased to have the same or adequate effects.
A sub-sonic .50 cal 600 grain bullet (think .50-70) would be suitable for deer and more suppressed.
Of course, you’ll have to be a better shot, as hold over will be significant even at 300 yards.