What is the best way to build a roof over a bar on my deck?

Well Bob, Seems that you thought this through. The first thing that I thought of was it`s a 2nd level deck. Adding any kind of structure on that 2nd story deck will add a lot more weight on those deck post and beams. Make sure that the beam is notched on the 6"x6" deck post going into the ground. Writing about the ground brings up another thought; is the original concrete footers going to hold that 2nd story deck roof. I started to remodel a owners attached 'add-on' to there old deck, like you are going to do and found out in the middle of there project that the add-on had sunk into the ground 8", due to the first builders not checking on the deck footers. And the project had to go on hold until the footers had to be redesigned(engineered). Just a heads-up when adding on more weight onto a existing deck footer. Now if your going to do this with a wooden roof system, then I "highly" recommend getting it engineered by a True 'Engineer' and having a permit will insure that it pes all codes and will stay attached to your house forever. "No one" likes to find out later on that the structure is sinking into the ground due to the fact that the one building the structure didn`t know anything about " barring loads". And how they effect your structure your building. A retractable awning may be the way to go here and save you all that work and money to do this project right from the start. Sorry for being total honest here but that`s just me :-). Hoped any of my info. helped keep you safe and smiling around your bar for a long time...