There are ways to transfer files to dos computers using a serial cable. Laplink and fastlynx both are able to do this. Basically you transfer control to the remote computer using the dos ctty command. The problem is I have no idea if laplink or fastlynx executables are Rainbow compatible. Whether they just use DOS or if they try to write to the hardware directly. The other issue would be that those are dos or windows programs, so you’d need a virtual machine running windows (or maybe dual boot boot camp) if using a fruity computer.
Here is some documentation:
http://www.minuszerodegrees.net/transfer/fastlynx33/sl_transfer.htm
Here is some documentation:
http://www.minuszerodegrees.net/transfer/fastlynx33/sl_transfer.htm