How many grams of Ba(OH)2 must be added to 2.37L of water to make a saturated solution? I got 2.03 grams. Is this correct?

It depends upon what you used for Ksp. I looked on the web and found 5E-3 for Ksp.

Use your Ksp, divide by 4, take the cube root, multiply by the molar mass Ba(OH)2, and that times 2.37 should get it. That's more than 2.03 g; however, remember the Ksp you are using may not be the same as above.