My experience is that the humble 2N3904, depending on manufacturer, can make an excellent low leakage diode and, being cheap as chips, are inexpensive to select the good ones out from a big bag/reel of them. I've had good results from Fairchild ones.
This is where I ended up actually. I've got a bag of Fairchild 2n3904s. Problem I have now is how to measure leakage at picoamp levels. Had my head in Linear data sheets for the last two days working out how they do it. All of my kit loads it too heavily.
If you don't have a dedicated picoammeter, the easiest way to do this is to construct a little battery powered transresistance amplifier you can use with a multimeter. Dead bug construction style is the norm for this so as to eliminate leakage paths. The classic op amp to use for this is an LMC6001 (25fA input leakage guaranteed, 10 fA typical) but they're expensive - around £10. A cheaper alternative ( < £1) is the LMC662 (2-4 pA guaranteed, but 2fA typical input leakage) and hope you get a good one or select from a few. Next hurdle is a good stable high value resistor for the feedback path - 1G or 10G. The last hurdle is you're going to want to protect that highly sensitive input, which means selecting some low leakage diodes/JFETs/BJTs. Recursion - see recursion.
Once you've built something you'll enter into the fascinating world of low level measurement where moving near your bench can change readings, you start fussing over humidity and temperature and the cat becomes even more of a hazard to work in new and interesting ways.
If you haven't already read a copy I recommend the Keithley "Low Level Handbook" downloadable from Keithley's (Tektronix) website I believe.
Finally a two part article from Paul Grohe (The late Bob Pease's technician) in EDN to get you started: