Can I offer free delivery as a promotion?

Yes, and it is a setting rather than a coupon. Open Settings → Ordering rules and fill Free delivery over with the cart amount that earns it. Below that amount the customer pays the fee for their building; at or above it the fee is zero. A coupon cannot do this today, because coupons discount the food as a percentage or a fixed amount. Watch it on your Dashboard: the average order usually moves up when the threshold sits a little above it. Say the number on your page and in your campaigns, because a free delivery nobody knows about buys nothing.