I am looking to do a diorama depicting an Oklahoma family leaving their home during the dustbowl with all of their belongs strapped on or in the car and I am needing a vehicle from that time period, late 20's/early 30's. What car kits are available from that time period? I am also wondering what I might be able to do for a mattress to strap on the roof. Maybe some doll house furniture?

Most of the kits representing '20's -30's vehicles tend to represent the more "high-end" manufacturers (i.e. Bugatti, Dusenburg, etc.) and therefore are not the best suited the the diorama you are planning (although a dust-bowl family leaving in a Bugatti Royale does present an amusement factor...)
That said, there have been a fair number of Ford Model T and Model A kits produced, many of which are still available and would be ideal for your diorama. AMT has produced several T kits in 1/25th. The "Police Car" issue (which also builds up as a standard Phaeton) is currently available.
If you want something bigger, Minicraft has several Model A body styles available in 1/16th, and they build into impressive models.
Your idea of using doll house furniture is good. I think most doll house furniture is around 1/20th scale. The only antique car kits I'm aware of around that scale are the old Hubley metal kits. These are easily found on evil-Bay.
Good luck with your project

They did a 29 Ford Coupe, a couple of Model A sedans, a couple late model Model T's. You could even use the Beverly Hillbillies car as a junker. Revell has a couple of I think 29 and 32 Ford kits as well.

Check with model round up they might have what you want Bill.H