Identify item as sold out only for a particular market

[Bryan46]

I sell products to two different markets and have a product that I would like identified as "sold out" in only one of the two.

Currently I use a fulfillment partner and they automatically update the inventory but it is universal - meaning that although I have product in one market but not the other, it shows the sum of the two.

Because of this, my product doesn't identify as "sold out" in the market I want it to.

Any suggestions?