Wife is recoil sensitive.
Two things to get right that are more important than cartridge:
1. Stock Fit
Especially LOP. My wife likes 12.5". A nice recoil pad included in that 12.5" is also indicated.
2. PAST Recoil Pad
At least from the bench. Get the thicker, wider one. Made a world of difference.
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Cartridges
Both Federal and Remington offer reduced recoil .308Win loadings. Rem has a 125gr spire point good for longer range shots, Fed has a 150 or 170gr RNSP for thump up close. Hornady has one, too, IIRC. Your current rifle in .308Win, with a smaller stock, and her wearing a PAST pad, shooting reduced recoil loads may be a solution.
I own a .243Win and my wife has taken game with it. It works, but you really want a premium bullet if you value penetration. 100gr Nosler loaded by Federal is good hog medicine. Hornady 90 or 95gr SST is more accurate and I would trust versus less stout critters. [The Ruger American Compact rifle is a good inexpensive rifle...if you buy a Boyd's stock to replace the awful factory stock. Paid $325 for one.]
Had I a do-over, I would prefer she had a 6.5 Swede (or 6.5Creed or .260Rem) as a do-all rifle from bitty critters up to Elk.
But, really, lots of low-recoiling deer cartridges will do the job:
.243 Win
6mm Rem
.260 Rem
6.5 Creed
6.5 Grendel
7mm Mauser
.257 roberts
7mm-08
Good lcuk.