While I'm not an expert on upholstery, here is the information I gathered up while researching this topic for the car I'm restoring. I'm sure others can chime in with additional information and/or correcctions:
According to the Master Parts Price List, the 1929 Phaeton came with the top fabric in either "black" P/N 114261, or "whipcord" P/N 114245.
"Whipcord" is a strong worsted or cotton fabric with a diagonal rib, a sort of canvas. The most popular modern equivalent is made by Haartz and is called "Stayfast".
The "black" is an imitation leather (modern equivalent is vinyl) with a pattern called "Bison Grain". It comes in "long" bison grain and "short" bison grain and is available from a number of upholstery material suppliers and was also used for the top inserts of closed cars as I understand it.
The Parts Book does not say what fabric was used for the seats and trim, but it is probably safe to assume that the same fabrics which were used in 1930 were used in 1929. The two available fabrics were both "imitation leather" -- what we would call naugahyde or textured vinyl nowadays -- and it was available in either Gray Spanish Grain (P/N 114273) or Pebble Grain (P/N 114287). I have seen several restored 1929 Phaetons and am working on one myself. All the ones I have seen used the "Pebble Grain" imitation leather, which is a black vinyl on a cloth backing with a distinctive, somewhat unusual pattern. It is available from SMS Auto Fabrics <info@smsautofabrics.com>, but is very pricey. I found a dead ringer for it in a local upholstery fabric supplier's stock and used that in my 1930. I plan to do the same in the '29 I'm workiing on now. My understanding is that woven fabrics were never used in the interior of open cars due to the risk of getting wet -- open cars of this era used either leather (luxury cars) or imitation leather (popular cars).
I hope that helps............ that's about all I know about it, and even some of that may be wrong. Others?
All the Best, Chip