Unfortunately, I think for the most part, bigger deals & discounts are rare on the Apple TV 4K.
Now occasionally, a retailer Best Buy or Target may have a sale, but you'd be looking at the same "couple of dollars" off that you're finding now. I don't think I've seen substantial discounts.
I picked up mine when Direct TV Now was having a promo.....free Apple TV for 3 months of prepaid service. That came out to $120, which I believe at the time was mentioned as being the lowest price point one could find it at. (Sadly that deal ended)
You may want to look to see if Apple has any refurbished models. It might not be huge savings, but any amount could be helpful 🙂