usb daq device to rs232
USB to RS232 or TTL Serial are USB Slave/Peripheral Devices. They need a usb host to work. It does not work backwards by themselves.

Your three options are 1) if the existing device already uses a serial to usb device inside, you can modify it by removing that part and wiring to the existing serial connection. If the serial inside is TTL, you would need a TTL to RS232 level adaptor.

2) If you don't want to modify the device, and it is a simple CDC/virtual serial port device, a small linux computer with a usb and a serial port can be set up as a pass through device. Like 10~20 dollars and an hour to set it up if you have linux experience.

3) If the device is not a simple serial port device, requiring special drivers and software to work, then you are looking at a problem that will require a high number of man hours to reverse engineer and implement, if not money.

A fourth option is replacing the DAQ with one that suits your need.