Regardless of the chosen finish, note that the coasters' end grain is very absorbent, so a few coats might be required to get a complete covering. Also, the finish requires an adequate time to dry before use.
In this case, a log cut from a branch of old Eastern Red Cedar (or Purple Heart Cedar) was used. But there are so many other choices. The main criterion is completely dry wood, otherwise the coasters might shrink and split.