Easiest is ringing up your FFP. It may help if you are prepared and know of alternative partner airlines or routings to suggest.
Otherwise there are a number (reducing sadly) of availability tools, which you could use (look up the operating airline rather than your FFP's airline) - but most dont show award availability; and as many have noted the availability may vary depending on which FFP it is being paid for (by miles) and also perhaps by status.
So, sorry I am not aware of anything that could automate your search.
The other option is to use
Randy's
www.awardplanner.com and let them take care of the hassles for you.