Is this possible without any sort of ladder logic? Are you saying that the PLC only needs a couple conductors from its output to a pair of the inputs on the VFD?
The program that I posted previously (Post #30) is the Eaton EZ ladder logic, similar to what you will need, whether it be Untronics Jazz, or Eaton EZ, or Omron ZEN, or any of the hundreds of other small available PLCs.
Yes, indeed, you only need about 3 conductors (for PLC to VFD): 1 from the COM terminal on your VFD control terminals to the Output COM on the PLC, and then from the PLC, 2 output conductors back to the VFD for "Run Forward" and "Run Reverse".
EDIT: I looked up the Jazz Jz10-11-R10, and see that it does not have a common output terminal, but instead has two terminals for each relay output. So if you use Outputs O0 and O1 for your Run Fwd and Run Rev, then you would jumper the VFD Com terminal to Jazz terminals 1 and 3, and connect Jazz terminal 2 to the VFD Run Fwd, and Jazz terminal 4 to VFD Run Reverse.
(Most VFDs have a built-in control voltage on the COM terminal, so you need dry relay contacts on your PLC). You would set up your VFD so that the absence of a Run command would be equivalent to a STOP command. That's all, no need to get into Modbus or some other comm protocol for this. You could of course, if you want to make it harder, more complicated, and more time-consuming to set up!
I see that your Unitronics Jazz is made for 24 VDC only, so you need to make sure that all your inputs are 24 VDC-compatible, and you probably will need the extra Jazz Add-On module to give you the capability to connect to a RS232 port on a computer. It appears that the Jazz only has 9-pin serial port comm capability, so if you have to connect to a modern computer with only USB ports, you will need a compatible USB-to-RS232 serial port adapter.
Is there a free download of the Jazz software? If so, I would like to get it and try it out. Does the Jazz have a built-in Simulator Mode as in the EZ and the ZEN, so that you can test your program to see if it runs (before actually hard-wring the Inputs and Outputs)?