Hi Nicole,
You can use the DC test as the numbers given in the datasheet Electrical Characteristics table are for DC at a gain of 1 and also at a gain of 32. However you must also consider the noise within the measurement process. Also, your measurement result is only as good as the performance of the test equipment used (such as the stability of the voltage source and accuracy of the voltmeter).
Using the AC test, you must also consider the affects of the digital filter in the measurement result. The AC testing that is done is with respect to power line frequencies, which is the normal mode rejection characteristics. The table of results for these tests is shown in Table 9 of the datasheet. I will state again that your measurement results are only as good as the test equipment used. You may see added noise and distortion as a result of the signal generator used. You probably want to take a lot more data points, such as 8-16k instead of 512. Also, you cannot use the SNR numbers from the FFT as the SNR would relate to the differential input and not the common mode input.
In either case, the device is specified in the datasheet and is tested as meeting a minimum CMRR of 80 dB, and typically 90 dB at a gain of 1 with DC measurement. This could be better depending on the device tested, but will not be worse throughout the operating temperature range of the ADS1248. So I would not discount the original numbers that you had calculated, although it does seem better than what I would expect. You might want to retest the DC measurement and go within 90% of full-scale at the DC measurement points for the input. 90% would be about +/-1.84V for a 2.048 reference and a gain of 1.
Best regards,
Bob B