You can use this program:
http://www.calcitapp.com/AVIAddXSubs.php
This program will allow you to have the subs "attached" in a single file, not hardcoded. But if you have a Divx compatible player you will not know the difference.
Another option is VirtualDub, which will recode your avi with the subs hardcoded onto the picture. It's a lot more difficult to use, but does a nice job. I use it for hardcoding subs for use on my PDA, which does not have subtitle support. You can read about it here:
http://www.virtualdub.org/index
LeapinLar