Rainbow's almost done RS-232 wise, you just need to hook up the transmit from the uPD7201.

Find this:

MCFG_UPD7201_ADD("upd7201", XTAL_2_5MHz, 0, 0, 0, 0)    // 2.5 Mhz from schematics
MCFG_Z80DART_OUT_INT_CB(WRITELINE(rainbow_state, mpsc_irq))

Add these two lines:

MCFG_Z80DART_OUT_TXDA_CB(DEVWRITELINE("rs232_a", rs232_port_device, write_txd))
MCFG_Z80DART_OUT_TXDB_CB(DEVWRITELINE("rs232_b", rs232_port_device, write_txd))

And that will enable the Rainbow to transmit on both RS-232 ports.