I think more people know what AC is than you think. I remember the Seinfeld episode, where Jerry was asking the guy who had an important race to attend the next morning what music he wanted to wake up to and went through a list of formats. The last choice he mentioned was "how about Adult Contemporary?" and the guy was like "Ok Adult Contemporary - just pick one".
In other words, I think most or many people who are familiar with or fans of Adult Contemporary could "figure it out" for themselves, in regard to the "AC". It was popular enough for Seinfeld to use it in his show, trusting that most people would "get it" when he said it. The least that could happen is that the "Your AC Station" could just become the known slogan for the station and becomes its signature trademark, whether or not people actually know what it means by definition - sort of like how people hear "KEZ" and they automatically know which station to tie that to, despite the fact that they have no idea what the letters "KEZ" are all about. With the amount of stations with no slogans at all these days, I'm sure "Your AC station" wouldn't hurt anymore than having no slogan at all.
Ok, I am just making an 100% uneducated guess here, but I truly believe "Adult Contemporary" is a well known, and even a nearly famous phrase that most people would either understand or be familiar with at some level. I think it's well known enough to the point where people would know that this is what "AC" stands for. If some folks don't know it, then they can always google "AC" and... well, obtain some new knowledge about air conditionings. It's pretty much a no lose situation all the way around.