Are you thinking USB serial or RS232 serial? I'll assume USB.
I haven't looked for any of that kind of hardware recently. A few years ago, I did a USB to parallel project using the Elexol USBIO24.
https://www.elexol.com/IO_Modules/USB_IO_24.php which has become rather expensive.
Another module I have used is the USBmicro U421, which is much cheaper.
http://www.usbmicro.com/documents/2CDECB6069BC98A8B0B408E789A25B26FDF6DF71.html
But realize that either of these, or any serial to parallel converter, will pretty much slow your screen updates to a crawl.
Especially because the controller in this display requires 'status checks' before writing data bytes, so the interface must be bi-directional.
The alternative is to re-invent the wheel of a "smart controller", which would be a cpu with a USB interface and a few I/O ports. Then you program it in some language to impliment your invented or borrowed protocol, which takes your semi-high-level commands over the serial link, and draws the image widgets using the parallel interface to the CFAG. Lots of work to do this project.
Maybe there are already smart controller solutions on the market, I don't know.