For a tree, you'll have to frame around its trunk, leaving enough space for its ever-expanding girth. Use joists 16 inches on center with horizontal braces. A fast-growing sugar maple might put on 2 inches around its middle in 10 years; an oak, about half that much. Consult a local arborist and plan for the future shape your species will take. To prevent children and pets from falling into any gaps, consider building a simple square bench with a tall back around the opening.
Building beneath trees also presents upkeep issues. Those leafy branches that shield the deck can also—in certain climates—cause dampness and stimulate the growth of mosses that make boards slippery if not scrubbed down frequently. Work with a tree service to inspect and prune away weakened overhanging limbs to prevent them from falling and taking off the corner of your deck or injuring someone. Update your homeowner's insurance policy to cover damage to the deck, not just to your home.