How to measure nano-amps easily?
Put a suitable resistor in series, and your DVM (in voltage mode) over the resistor.

For instance, a current of 100 nA through a 1M resistor will give you 0.1V. Check the input impedance of your DVM, for this to work it must be >> 1M. You will probably need a switch to short the resistor for the period that your target is not yet in low-power mode.

Another way would be to use a known-sized capacitor as power supply and see how fast it discharges. Again, your measurement instrument must have a high impedance, otherwise it will  disturb the measurement. You might get around this by connecting the voltmeter to measure  the voltage only at specific moments.