Thinner plywood usually does well.

The veneer appearance is often not that critical since the books block most of the visibility, but Constantin's sells large pieces of pressure sensitive wood veneer if you need to match something up (and are willing to pay).

It can take some experimenting to get a finish that matches close enough ion color, but between pigment stains and aniline dye you can make the general color match usually, if not the figure of the wood.

Thin plywood. You can usually find 1/4" rotary saw red oak at your local big box store. If you want anything else, you'll need a specialty wood supplier.

Then stain/finish it to match the rest of the bookcase.