As an example, I recently installed such spoiler tags on my site. You can view a post with one
here. (I'm not trying to promote my site; I just thought it would be helpful for people to see an example.) It's something I also use quite frequently and it's great for posting larger images that would otherwise stretch the page or take ages to load. :3
Here is a basic BBCode for phpBB with
this fix to the code posted in that discussion. Or
here is a mod. Those were from a basic search if you (management) were going to seriously consider it. I'm not sure how much you've modified the code for this forum to suit your needs.