Dillard's does not offer coupons. The closest thing you will get to a coupon with Dillard's is to wait until the end of the month when they run their "additional % off" sale. Typically, these are the last "push" days of the month and the discount can be either 30% EXTRA off of a sale item or 40% EXTRA off of the sale item. Since this is January, the percentage this month will be 30%. This is also available online, but the selection is very limited and there is plenty in the stores.
FYI: These sales do NOT happen every single month, depending on what holidays etc. are at the end of the month. Typically, they will not run an additional if there is another big shopping event that will bring in the crowds anyways (i.e. Easter this year). Although, keep in mind that stranger things have happened and Dillard's like to do things their own way.
There are also special incentives for Dillard's Credit card holders. Such as a preview day for the sale and special offers inside your statements (free gift wrap), but the rewards have changed in the past years, so the value isn't as good as just shopping during the sales.
There are major bargins to be found at Dillard's, just have to look around a little bit and ask the associates what THEY are buying... they usually don't buy until something is a REALLY good price
Hope this helps!
P.S. today is Cardholder day so the sale will open up to everyone tomorrow.