So far I've never managed to get any relevant historical information out of Zeiss themselves, except for bits that pertain to Opton/Oberkochen. They managed to lose what was left of their Jena archive and museum over post-reunification squabbles, and anything Zeiss Ikon went other ways or was destroyed as well...
The patent was registered in Germany in 1935, the first coated lenses were demonstrated at the 1936 Olympic Games - Zeiss obviously geared up for marketing them in 1936, but somehow did not make it. Just why is hard to tell now, with most documents lost and a long history of blaming everything on the Nazis - personally I guess that it was a matter of technical feasibility and bringing it from lab scale to industrial dimensions rather than politics (with the patent, the cat was already out of the bag, so there would not have been any point in holding back mass marketing from that point on). That said, it might be that the Tessar may only have been available in coated in 1939 (when coating became optionally available for most lenses in their catalogue) - but not because coating was not invented or patented earlier. And the lens in question obviously was not sold originally coated in any case.
That, by the way, is NOT Zeiss, nor anybody affiliated with them, but Henry Scherer, a independent, strongly opinionated (and often plain wrong regarding facts) Contax rangefinder repairman in the US.