Thanks to all for your help. I did try bigger triangles but that didn't seem to do the trick. I came across this tute by Bonnie at Quiltville:http://quiltville.com/sqinsqtutorial.shtml. She has a chart for different sizes, and her inner square for a 5" finished block was 4", whereas the pattern I am using called for a 4 1/8 inner square. Bonnie also said to use bigger triangles and use the Easy Angle. Anyway I tried both size inner squares and bigger triangles and couldn't get it to come out with a 1/4" seam, so that is why I think paper piecing may do the trick.

As for placement, fold the square in half in both directions, kinda firmly, so you know where the center line is. Then, when you place your triangle on the square, match the point of the triangle to one of these folded lines. This makes sure the triangles are centered on the square.