I actually found what you need here through an online vendor I've never used. For the M1A it's called a stock liner and it comes with screws.
Your Source for Service Rifles: M1 Garand, M1 Carbine, M14 / M1A & AR Types
www.fulton-armory.com
And below is a wood stock accessories kit with additional parts you may need.
Our M14 gunsmith at Fulton Armory handcrafts the most exceptional rifles across the entire United States. Shop your source for service rifles, parts, tools, and more today at Fulton-Armory.com.
www.fulton-armory.com
The screws will need a special tool to install them which I added below.
Used to install or remove stock liner screws, fits a socket wrench or magnetic tip screw driver with 1/4 Hex Drive.
www.midwayusa.com
I hope this helps!