In the ADXL356 datasheet, the AD7682 ratiometric ADC is suggested as a a direct interface.
Are there any other ADCs which can be use to interface directly to the ADXL356?
Can you tell me a little bit more about your application and why the AD7682 doesn't work in your case? For example do you need a higher throughput converter or simultaneous sampling? This would help me narrow down the choices that will be best suited to your specific need.