On the Serial Pi Plus there are two spare channels on the MAX3232 converter chip which are connected to the four solder pads next to the chip. One channel is an input and the other is an output so you should be able to connect the spare output between a GPIO pin and pin 4 on the DB9 connector.
You will need to connect pin 14 on the MAX3232 to pin 4 on the DB9 connector and pin 11 on the MAX3232 to a GPIO pin. You can then use the GPIO pin to switch the output between +5V and -5V which should hopefully work for the DTR input on your serial device.
The photo below shows which pins you will need to connect. It may be worth checking the output of pin 4 with a multimeter to make sure it is working correctly before connecting your device to the port.