Daisy-chaining two ADC with SPI protocol
Thank you for all your help. Unfortunately neither of the suggestions fixed my problem. On point was indeed the timing. I adjusted the SPI clock-rate to cope with the 50MHz of the ADC.  With the adjusted clock-rate I got a proper answer from one ADC. Furthermore I checked the timing constraints with the Oscilloscope and they were all good 1. Also, I tried to read the ADCs asynchronously, which confirmed the assumption, that one ADC is not working properly. Since the board was already built, I was limited in testing the ADCs one at the time I ended up building a new board with a different ADC.

Oscilloscope Screenshot. CNVST: blue, SCLK: yellow, DIN: green, DOUT: red