DISCLAIMER: This may or may not work to transfer designs to tajima's via a serial connection!!!
No clue if this will actually work with your machine or not but similar settings work very well with Toyota embroidery machines so it's worth a shot.
Download and install Embroidery Fonts Plus: http://www.embroiderytools.com/free.htm
Configure your computer's COM port. To do this(assuming Windows XP), goto Windows "Start" --> "Control Panel" --> "System" --> "Hardware" --> "Device Manager" --> "Ports" --> "Communications Port (COMx) - where "x" is a number typically COM1, and then "Port Settings".
Bits per Second: 9600
Data Bits: 8
Stop Bits: 2
Flow Control: Hardware
Run EFP, goto "File" --> "Open" and choose the DST file you wish to load. It should open in a black box inside of EFP. Go back to "File" --> "Send to" --> "Tajima Emb. Machine" --> "Via communication port"
On the embroidery machine, enter the command to accept a file from the serial connection. Consult your operator's manual for the specific sequence to use to accept a file over a serial connection. Maybe use a 3 or 4 SET instead of the 5 SET used with floppy disks. Cross your fingers and hope the data transfers. After receiving the file, control will be returned to the operator and it's time to enter your needle sequence.
Hopefully that will work. If not, you're only out some time it takes to download, install, and configure some software.