The only way that comes to my mind involves a little bit of work and I'm sure is not the best one, as it requires ripping your DVD to another formart (.avi) and then back to DVD format with the new subtitles. But since no one else has posted, here it goes...
1) Rip the original DVD to your computer to a .avi format
2) Download the subtitles (or CC) files from the internet, put them in the same folder as your .avi file and rename the file to be the same as the .avi file (except for the extension, which should be .srt
3) Use a transcoding software such as ConvertXtoDVD to reconvert the .avi file to a DVD format. ConvertXtoDVD should recognize automatically that there is a subtitles fil and include it. The software also will burn to a new DVD
Again, this I believe is far from optimal...I'm sure the experts here will be able to give better options...