The Credit Union of Ohio made buttons for two or three seasons, all of which included games with Penn State. I have only identify the 2009 and 2011 buttons, but I assume a 2010 button exists.
There are also many one-off Ohio State buttons, but I am unsure if they are part of larger sets.
Ohio State makes BEAT TEAM buttons fairly regularly, but I typically don’t consider those to be “slogan” buttons even though they include the game date because they are fairly generic.
Penn State made anti-Ohio State buttons
We Are "Pin" State 