Measuring a huge resistance on low voltage
You can do what you want, but it won't be simple. Scratch that, it will be fairly simple, but it won't be easy. As von Clausewitz said, "In war, the important things are very simple, and the simple things are very difficult." It applies here as well.

Actually, it's not as bad as it could be. Your nominal current is 250 pA. You can get op amps with bias currents in the 1 femtoamp range, so monitoring your current is certainly possible. I recommend you start with Bob Pease's "What's All This Femtoamp Stuff, Anyhow?" http://electronicdesign.com/test-amp-measurement/whats-all-femtoampere-stuff-anyhow followed by "What's All This Teflon Stuff, Anyhow?" http://electronicdesign.com/test-amp-measurement/whats-all-teflon-stuff-anyhow

The devil (or God, depending on your background) is in the details, and at these current levels details matter a whole bunch. You'll need to clean your apparatus with alcohol to get any fingerprints off, and grounding will take on a whole new meaning for you.

But it's certainly possible.

Basically, you're talking about making a picoammeter, and you can buy those commercially. Here, http://www.rbdinstruments.com/products/picoammeter.html?_kk=picoammeter&amp;_kt=3ce3e0b6-02d3-4edb-8960-2273c533a323  for instance, is a cute little USB unit, but I'd be surprised if you can get it for less than $1500 - or maybe more. You can try eBay, and get rather cheaper than that.