How To:

Not as difficult as it may seem. It's not uncommon to build the deck around the tree (figure A), as well as a trellis above with the tree growing right up through it.

The idea is to build a collar around the tree. To do this you will  need to provide more support for the frame and joists that you will have to cut out for the tree trunk. It's a matter of adding adjacent joists of smaller lengths that accept the load of the area in the back and front of the tree.  All joists must be supported.  Just remember you are building up the frame around the tree to support  joists.

The size of the frame is dictated by the size of the tree and it's age.  If it's a young tree, then allow for growth by building a larger frame. A good rule of thumb is to give a young  tree at least 5 inches in diameter around it's trunk, especially if you are building the deck near the ground.  For older fully grown, trees 2-3 inches around the deck is good.

Another consideration is  if the tree you are framing will  also extend up through your second story deck, obviously it too will need to be framed. Think seriously  before proceeding because if a large gust of wind hits that tree, it could force the tree  to sway in the wind and push the tree against the deck and possible pulling it from the house..