When giving away coasters I made, they were usually just tied into a set with ribbon or burlap twine. However, for more special occasions or people, I also made a custom coaster holder that entailed a bit of tedious work.
The holder was a "V-shaped" tray tilted at a 30 degree angle, made of walnut and doweled together. The tedious part was doweling the necessarily thin walnut pieces.
To begin, the walnut was ripped and planed to 1/4" thickness and sanded. The V was made of 1-1/2" and 1-1/4" widths, cut to the length of 6 or 8 coasters. The butted joint was glued with Tightbond and after it was dry, reinforced with (4) 1/8" dowels. The front of the V was supported by a 3/8" dowel turned from walnut (or purchased) blind inserted into a pocket in the bottom of the V to elevate and support it. The front and rear openings were closed with more walnut pieces. The front's piece was an oversized V to match the shape of the sides, but with rebated corners. Once glued in place and set, it was reinforced with (2)
1/8" dowels per side plus another at the bottom of the V running back to reinforce the 3/8" dowel in the pocket behind. (See below for how the doweling was done)The rear piece was slightly taller than the front and the upper part was of a similar rebated shape. It was taller to support the back of the coasters, being tipped backward. Behind was a wedge-shaped brace in its center to further prevent it from tipping, along with a 4" wide square cut bottom to prevent side-to-side tipping. All joints were first glued, then doweled and sanded.
For drilling a 1/8" hole in 1/4" edge material, a typical drill and bit would not work. The slow speed of the drill would permit the bit to catch on grain and not make a hole where desired OR to drift off as it got deeper. I had two solutions and both worked well. The first was to use an air powered right angle drill cobbled together from an angle grinder and a Jacob's chuck. The other was to use a Dremel mototool with an 1/8" collet to hold the bit. In both instances, I tried using both a typical twist bit and an augur-type bit. The lead point on the augur-type bit helped some, but the titanium coated twist bit lasted much longer. The faster the drill bit turned, the more accurate the holes were.