I misunderstood your post sorry...
The problem marco brought up with cookies is easy to solve, just use the same copy of php files for both forums, as long as you have a license for each this won't matter.
Exactly how much of the forum do you want to change between sites? If you simply want the style to change it is not hard to do as long as cookies don't become a problem. To avoid the cookie problem I would just set two durring login (once for each domain).
With some code modification you can pull it off, but it all depends on how far you want to go with it.