You will find most furniture is hand made which means you can have it made to your specifications.
Perhaps the souks are a good start although these are scattered over a large and will take up quite a bit of time searching.
What I have learned about the souks is they are divided into different sectors, ie in one area they sell leather, in another wool and so on.
I am unsure of where furniture is made off hand although asking a trader in the souks (rather than have a shopping guide) will get you in the right direction.
If I come across any info I will be in touch.