If I remember correctly (it was about 8 years ago), when my boxer was on prednisone she did have some diarrhea, but it was only the first few days of taking it.
Another thing I'm wondering if could have caused it also, is we gave him Rabbit last night, which is the first time he has tried that, he didn't like, but I mixed some shredded cheese in with it and he ate most of it then.
As a human RN, I can tell you that Prednisone, although very effective is very hard on the body. It raises blood sugars and causes obvious mood changes in some patients, such as anger, irritability and occasional psychosis (my favorite!!). Makes one wonder if dogs get same mood changes with it