How do I drive pin 2 on my 555 IC low so the one-shot timer will fire, using an IR sensor in place of my pushbutton switch?
The 9 V supply is problematic since the IR Rx is limited to a 5.5 V maximum supply.

Note: You also show the IR RX connected to 6 V on your breadboard ...this may damage it. 

If you alter the schematic to that shown below, lowering the voltage to a more acceptable level, it should work.
You could use either 3*1.5 V cells or a single Li-Ion cell providing you don't have a high voltage LED on the output.     



I'm not quite sure from your question what result you want, but the output of the IR Rx will be a string of detected IR pulses from an IR remote. The output signal will repetitively re-trigger the 555 monostable, so the LED will likely come on for longer than you think.
If all you are looking for is an indicator of remote activity then this may be ok.