A reader (Dave from licomputerhelp.com) plotted a graph showing MLS inventory; thanks Dave! He gathered archived data from web.archive.org and plotted the inventories since 1999 at the end of each quarter the best he could using the total properties listed in red on the home page of mlsli.com. The only problem I see with the chart is that it shows not only single family houses in nassau and suffolk counties; but also shows the inventories for condo's and timeshares, etc. not only on Long Island, but brooklyn and queens as well; but that's the best you can do with the data provided. We both agree that it clearly shows the inventory is rising on Long Island.
As high as the inventories show, these are only non-exclusive listings. To get the complete inventories on Long Island, you would have to also get the exclusive listings (on realtor's sites) and the FSBO's; both of which aren't listed on the MLS.
Update: I have isolated Long Island (Nassau and Suffolk) from the MLS. These inventories are updated daily and only reflect MLS inventory for single family houses in Nassau and Suffolk counties. You can access the data here.