How to make a constant current sink in the pA-nA range
Linear have a Precision Nanoamp Bidirectional Current Source application note that may be of interest.



Figure 1. This circuit sources and sinks just nanoamps of current with precision due to the low input bias current of the CMOS op amps. A buffered difference amplifier and an integrator force the voltage across a 10 megaohm set resistor to be 1/1000 of the control input voltage in either polarity.

Whether this is suitable for your application is difficult to say due to the lack of information supplied. It has the advantage of not requiring any ramp generation or precision capacitors.