Your drawing of the AD1937 in Single-Line Daisy-Chain TDM mode for both ADC and DAC paths is correct. I would make one small addition: the AD1937(First) has ASDATA2 and DSDATA2 pins. The ASDATA2 pin of AD1937(First) should be connected to GND on order to keep the ADC TDM stream clean as it is originated in that part and sent to AD1937(Second).
How many channels will be in your TDM stream? What sample rate(s) will you be using? Which part will be the clock master? I will be happy to help you with your register settings for this system.