Felt recoil is caused by a lot of things. The hardest recoiling rifle i ever had was a Savage 110 in 7 mag, stock design/fit was the problem. Now i shoot three different Rum chamberings, yet found my Tikka T3 30-06 to be excessive. A Limbsaver recoil pad tamed the T3, and its now my go to rifle.
Trying to find a actual light recoil rifle, just specifically for Deer may be a case of experimenting with specific rifles...not endorsing a make and model. Take steps to handle recoil at the range, then try a few rounds without aids from hunting positions. Remember that one feels recoil at the range, but not when shooting at animals.