What type of rifle is your 308? How much does it bother her?
This here ^^
Factory ammo or reloads? If reloads, try some 125 grain bullets at moderate velocities. I wouldn't lie to ya, there will be LOTS of energy at the other end to kill a deer with!
No need to wring the nuts off the cartridge to get it to kill whats at the other end, esp. if you are shooting mainly in close. Lots of the dudes seem to think their manhood is in question if they don't shoot the biggest baddest thing on the line. Since she isn't a dude, she won't be worried about that now will she?
.223 worked well for my needs and those of a new to hunting young lady that I helped, this year. She went with the .223 as she was adverse to the recoil as well. Not a caliber for shooting a deer in the bum with, more for being patient and choosing ones shots.
Some form of .243 ammo is usually among the selections at pretty much every boot-nowhere small town hardware store that still sells a bit of ammo, if availability is an issue.
One other thing to possibly do, is to get her out to the range for more trigger time on lighter recoiling guns, and work her way up, as it were. If the .308 is beating her up too badly, is it the gun (ergonomics), the load (lighten up), or her positioning and hold when shooting (send her to the range with another, experienced woman, to work that out, or have someone else have a look and help her). YouTube is full of vids of guys letting women do frikken horrible things with guns, and laughing at the result. Not sayin' you are that, but getting some advice that is not from you, may be helpful.
Cheers
Trev