I had a look at the data sheet for this device. The maker claims it is stable even with slowly changing inputs.
So, it might be input noise.
If your application is just using variable DC voltages, you could try common mode bypassing. You put a
capacitor between the inverting and non inverting inputs. Maybe 47 pF if it won't matter for the application.
This is a very fast chip, so it could be reacting to pulses on the input that would be hard to see with an oscilloscope.
You may be able to get a clue from the frequency of the output.
If the output is 60 Hz it may mean you need better shielding of the input wires. 120 Hz may mean there is a problem with hum from the power supply.