I haven't tried these cookies with a different oil, but an oil that is solid at room temperature may work.  If you have a favorite vegan butter or grass-fed butter (if you aren't dairy free), those may work. Just make sure they're at room temperate and softened when you use them.  Refined coconut oil may also work, but I think it would impact the texture and the cookies may not be fluffy and possibly have extra crispy edges.   ​I don't think oil that is liquid at room temperature (like avocado or olive oil) will work.