Optocoupler Issue - Not sure why it isn't working - help needed
Note: You are driving that poor LED very hard with 60mA typical current (the absolute maximum number). I would suggest increasing the resistor to at least 300 ohms- but more information on the VFD input is required to determine if that is okay or not. Possible consequences include rapid aging of the LED (the isolator will weaken in CTR over time) or sudden failure of the LED. Note that the CTR is specified at 1mA and 10mA. If you have no info on the VFD input you could test it at (say) 2mA and if it works go to 10mA (add some at least 2.5:1 safety margin to account for time and temperature changes). 


When the switch is closed (LED should be energized) do you measure voltage across the 62\$ \Omega \$ resistor? If not, there is no current flowing and the LED cannot work. 
Possible reasons include wiring, a bad component, lack of 5V supply or (more likely) the LED is connected backwards. Measure the voltage across the LED- it should be about 1.25V. 
Assuming the LED is conducting and the drive input is the type that accepts a dry contact, there should be some positive voltage present at the transistor collector (several volts) when the switch is open (or when the opto is disconnected). The voltage should decrease to much less than 1 volt (still positive) when the switch is closed. If that is not happening, there is something strange with the input, the opto-isolator has been damaged, or (more likely) the transistor is wired backwards (emitter must go to ground). 
Some inputs are not designed to accept a contact (such as a mechanical switch) to ground and require a logic input-- which means you need a power source on that side of the LED. It's not so common with industrial equipment, but a link to the manual would help. 
Why is the opto in there? Will the switch not work by itself? Or is there some mains isolation issue?