JDM programmers are dependent on the software used as to which PICs they can program. The 18F2550/4550 are supported in the software I have seen. Read the Advanced JDM Programmer link for some software.
Usually, JDM-style programmers need a real RS232 port because they make use of the real RS232 signal levels to make a voltage multiplying power supply. Often (most/all?) USB-Serial converters do not have the required output levels, so probably will not work.
However, Fragrance's Advanced JDM circuit is externally powered and does not depend on the serial port for power, so this one might work on a USB converter. Why not ask in that thread for advice on that matter?
Another alternative is this circuit, which generates its power supply from a USB connection (only power, not USB data, and you would need another USB socket for the converter) so again, this might work with a USB converter for the serial.
**broken link removed**
Please note that I have not tried the above circuit, or Fragrance's circuit, since I made my own JDM programmer a long time ago and programmed another PIC to make a better programmer.