Or how about these pretty stitched coasters?
Here are some pretty ones that appear to be painted on cork (I've seen some nice ones painted on tile, but those are heavier than what I'm looking for):
You can buy plain Zentangle coasters on Amazon (and elsewhere), draw or paint your own designs, and (if you like) cover them with something like Mod Podge to protect them (I'll bet you could even use heavy white paper backed by cork or reused cardboard).
And if you're interested in other ideas, here's a list of 30 DIY coasters (note: I haven't checked all the links):
Even if you don't need coasters yourself, they might make nice stocking stuffers. It's already mid-August. Christmas is coming!