I got my belly button pierced about 2 months ago and in the mornings I can get a little bit of pus out if it but its not yellow and there's no pain. Is it infected or just trying to get dead tissue out?

It sounds like the normal healing process to me; just make sure you're not over-cleaning (once, maximum twice a day) and just use saline solution/salt water to clean it. When you say you CAN get a little bit of pus from it, does that mean you're squeezing the piercing? I wouldn't do that, just clean it and it should heal up nicely on its own soon.