My wife mentioned that she was having this same problem with "Coupon Printer" software under Snow Leopard, so I decided to look into it. The version she was using came from
http://bricks.coupons.com/Download.asp . It downloads as as Mac .dmg file with a "Coupon Printing Installer" package inside. Running the installer always results in an unspecified failure (and then, of course, coupon printing does not work). I brought up the Console app to see if there were any relevant error messages recorded, and under "All Messages" I found several lines describing the failure. There was enough info that I was able to isolate the problem to the execution of a bash script named "postflight."
So using SL's Finder, I went back to the "Coupon Printing Installer" package and selected "Show Package Contents" from the context menu. From there I found the file "postflight" under Contents->Resources and opened it with TextEdit so I could see what it was trying to do. As it turns out, by the time the installer gets around to running this script, the installation is actually all finished and the only thing this script tries to do is restart the cups printing subsystem so that the newly installed files will be used. Naturally, it did not have any code in there for Snow Leopard and so it was just exiting with a failure instead. In other words, even though the install process reported failure, it was actually all finished except for restarting "cups".
When I realized this I just rebooted the computer (which obviously will restart cups), and sure enough, the Coupon Printer software is now working just fine with Firefox. It did not work under Safari, but I suspect it would have if I had started Safari in 32-bit mode, which I did not do because I like the performance of the 64-bit Safari process.
I don't know if everyone's "coupon printer" software is the same as the package my wife was using, but if it is similar, rebooting your computer may just solve the problem for you too.