Currently, the forum I use uses a USA time, rather than GMT. The admins are trying to get it fix, but apparently, it's something that'll be hard to change. I'm wondering if anybody may know how to change it to GMT without loosing any data through the HTML or any other possible way. Here's the site link to help: http://orb-central.com/forums/index.php
There should be a setting in the ACP which will change it for guests and all new members but current members will need to change it in their UCP. I can't think of any forum software that doesn't allow you to change the timezone so there should be an option somewhere.
I wouldn't be as simple as just a bit of html... It will involve editing the php code and making it change the time it puts in the db for each post when it is made.
Assuming the time is stored as a unix time stamp when outputting the time just take away or add however many seconds to get it to the to the correct time zone. i.e. if it is added at GMT and you want to show it as GMT+1 then add 60*60 seconds then output the date using date
Honestly, I doubt it (apart from what spyka wrote, assuming you know PHP and how the software is setup, http://php.net/date), as you say it's custom, we don't know how it's built, setup, etc. etc., so it's reallly hard to help you.
I think it's a custom software on many forums as well. For members to adjust it to their own time zone, they would have to go into their User Control Panel like everyone else said. That's the best I can come up with. Otherwise, I don't think there's anyway to change it entirely.