Is it possible to make a coupon get rid of the tax on an order?

Hi,

Well, the best would be to create a custom field of the table "order" and develop a small plugin to check what is entered in that field and modify the taxes of the cart to 0 by implementing one of the triggers when the cart is being loaded.
That would be the smoothest way of doing it. You could even allow people to use coupons separatly to that system.
Now regarding just coupons, if you have a fixed tax rate, you can enter the same value in the percentage field of the coupon, and if you turn off the taxes of the coupon, you should hopefully get something correct.
Maybe AWOCoupon (which integrates with HikaShop for more complex coupons) might have a better solution for that. So it's worth checking out with them.