Both the dough and the finished cookies were quite a bit more fragile than shortbread made with butter. I rolled the dough into a log before refrigerating rather than rolling out and cutting with cookie cutters as in SK's recipe. The dough was much more prone to shattering when I cut it off the log than regular shortbread is. I couldn't cut the cookies as thinly as I normally do for shortbread, which combined with the richness of coconut oil means you really just want one or two at a time, not seven. Whether that's a problem or a benefit is unclear.
After baking, the cookies were very liable to crumble completely, and I'm just eating them off of the cooling rack because they're too delicate to transfer. I'm guessing that there is some mixture of butter and coconut oil that will have the perfect combination of durability and tastiness. If you're in need of a vegan shortbread recipe, this is it. If not, you should try mixing butter and coconut oil for optimal durability.
Double coconut shortbread (adapted from here)
3/4 cup coconut oil, room temperature (or mixture of butter and coconut oil)
1/2 cup sugar
1/2 tsp vanilla extract
generous pinch of salt
1 1/3 cups all-purpose flour
1/2 cup shredded coconut, toasted (the really small kind, about the size of breadcrumbs, not the big flakes)
In an electric mixer, mix together the coconut oil and sugar. Add the vanilla and salt and mix. Mix in the flour and then the coconut until it kind of forms a dough. I had to turn it out onto a cutting board and use my hands to get it to come together all the way. Roll into a log and refrigerate until hard.
Cut cookies onto a pizza stone or cookie sheet. Try to get them as thin as possible without the dough shattering, which for me was between 3/8 and 1/2 inch.
Bake at 325 F for 15-20 minutes or until they look like cookies instead of dough. They won't brown as much as cookies made with butter, in my limited experience, so the usual "golden" cookie instructions don't apply.