You can't use this power supply in this experiment.
This unit maybe is very good for power supply, not for signal
generation.
Build divider 10k-Rsignal1-Rsignal2-10k( lower impedance is better, but will be thermal effects; 1% resistors will be ok).
Rsignal1,2=50..100 ohm.
Power this from AD7730 power supply (5VDC), connect these 5V
to reference input of AD7730.
Measure signal over Rsignal1 resistor.
Measure signal over Rsignal1+Rsignal2.
You must get stable results at least of about 2microV, maybe stable 13..14 bits of ADC.
This is very basic check of Your circuit.

About AD7730 settings- setup to low sample rate - try in range 30..60 Hz. Amplifier settings is not very important at this stage. By the way - what are Your default settings? What microcontroller You are using?


One suggestion - break traces between ADC and micro and put
resistors 200..1000 Ohm on each of these connections.
Make slower serial communication between ADC and micro .
If You have big power consumption in rest of circuit - turn off it, for example: dont use LED indicator - send data to PC terminal(better - trough optocoupler). Power board from accumulator, even from car.
regards