I 'm sure if you Google you will find lots of patterns for coaster holders or trays out there, this is just how I have done mine. Hopefully once you see the formula, you can customize it to what works for you!
Step 1: Measure the coasters width and the coaster stacks height. (this formula is for square coasters)
Step 2: Take those measurements and make the formula.
width of coaster + height of coaster stack x 2 + 1" = the size you cut the outer fabric and lining
So for this example my coasters are approximately 6.5" and 1.5" high
6.5"+ (1.5")2 + 1 = 10.5"
Step 3: Cut (1) 10.5" sq from lining fabric
(1) 10.5" sq from backing fabric
(1) 10" square of batting or the full 10.5" if you aren't worried about the extra bulk (you could add whatever batting or interfacing you wish for the desired firmness of the tray. )
Step 4: I used Pellon fusible fleece, and fused it to the backing fabric.
Place the lining fabric and the backing fabric right sides together and the batting if not already fused in place on the wrong side of the backing fabric. Sew all around the square leaving an opening for turning. (backstitch at the beginning and ending for stitch strength when turning)
Step 5: Trim corners and turn right side out, carefully pushing out the corners.
Step 7: For each corner fold your block in half on the diagonal, and mark the 1.5" in and down spot with a line for sewing. Stitch on that line, again backstitching for strength.