The rule is - that there aren't any rules!
I made some last week using thevinyl table protector material. I embroidered the design (not too dense) and then added a second layer beneath the hoop and stitched an outline (just a simple running stitch.) I cut them out about 5mm away from the stitching.
If you use fabric you could do the same but you would need a satin stitch border and some interlining or wadding. (Muftoflex has a good outline in DBC.)
There are lots of coaster experts around here - just hang around for a bit and the advice will flow!

I have just done some on felt. Stitched the pattern, added a second bit of felt underneath and then the outline. Then I cut round them. They are quick (OK not as durable as some I have made) and I hope they will sell on a charity sale!

I have done them with fleece. Stitch the design then at the step where you put the back on I also add a piece of iron on vinyl (it starts out sticky so I stick it here and iron down after all done) on the top to stop the moisture from damaging the stitching (and / or the table underneath).

I use any fabric. Linen look is great, muslin, chino etc... I put felt inbetween the two layers before I stitch it with the final die line. Have fun... Suzanne

Good question. I'm looking forward to hearing how everyone else makes their coasters.