For example I got the HomePod for 250 USD. Would love to pickup the Apple TV on discount but everywhere only seems to have it for a couple of dollars off.
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
I was also looking for deals on the Apple 4K TV, decided to go with Apple refurbished for $150, 32GB. It came today and was brand new in retail packaging not the standard white box. Comes with same 1 year warranty.