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.
Excellent cond. USGI buttplate assy, completely reconditioned (Duracoated inner plate, all other parts parkerized)
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!