The time constant of 30 seconds would point to something other than the op-amp. As noted by IRStuff, the time constant for a 68 mOhm resistance with a 10 pF input capacitance would be about a millisecond.
Even if you waited 5 or 10 time constants to settle, this is pretty short.
Does the 68 mOhm terminate on ground or on some floating point. Especially if this is battery operated, you might be seeing a power supply feedback component.
Are switching the power to the op-amp on and off? There may be some other compensation as simple as bypass caps that don't settle. And if the 68 mOhm terminates on anything other than ground then switching the power would be a problem for more than one reason.
What is the reference to the A/D. Are you measuring this drift with the A/D or with a scope?
Does the circuit have a single r/c approach to its final value, or does it simply take a long time to get to within the required tolerance? The 0.47 cap on the output, if electrolytic, could have enough memory to keep the output from settling for quite a while.
Consider using an inverting amplifier referenced to ground. This eliminates voltage changes at the input and so the input capacitance can be ignored. If you need a reference voltage, use a voltage reference chip that settles in milliseconds after power up.
These are just some ideas. Usually you will find what the real problem is in the process of eliminating potential problems.
DspDad