If the ohms of the sample are very large, the RC time constants can be surprisingly long. Minutes or hours is not out of question.
In these cases, it might be sufficient to define a procedure where you take the measurement after XX time of electrification. Such a consistent method would allow comparison of sample A to sample B, etc.
Unrelated: you may want to consider some shielding for the setup. With connections in open air, results are susceptible to EMI and charged particles from air. Simply walking past the setup can be reflected on the picoammeter.
Low level measurements handbook