We need more information. The nature of the signal is not clear to me. Is it a signal with a -1V to +1V range, for example, and you need to measure the whole range?
If the signal is 'unstable' you might need to fix it first depending on what you mean by unstable.
You must be trying to sample the analog signal.
How about shifting the signal to the range that can be accepted by your ADC.?
This is a common problem, so I think there will be many solution to this.
I believe there are also ADC that can helps you with this signal that you have.