ther are specifix DLL's that your program uses... try launching it on a fresh installation pc and it will output the required DLL's >.<
But yeah you can find the needed DX verion on the Dark game Studio DVD if you have it... I am not sure where you can download it through the TGC site...
but I guess you have it already lol...
I think what you need to do is perform a silent install of DX during the installer but this does mean adding the I think it was roughly 90MB file size to your program.
The DX installer found on DGS is a distribution edition... so you should be fine distributing it anyway... but best checking on that... though I believe all DX installers are fine... I mean to distribute... I think its DX 9.0c August 2008... can someone please confirm this? you could just find that Microsoft download page and link users to download it themselves.. but you can also find the information on that page regarding distribution with your own programs.
You can also just run the installer during install does not have to be silent... the libraries will just add the differences.
urgh hope this made sense and helped somewhat...
btw what are you using to make the installer?