Nylon UV stabilized rope. Climbing rope is expensive, but easy on little hands. Any rope rated for towing will do - you might want to put a hessian sleeve on the grip part for the rougher but cheaper ones. Use an eye bolt through the whole branch vertically, a wooden washer/rain shield on the top and attach both ropes to the eye of the bolt. This is the easiest way to level up the seat, and the kindest on the tree. A thinnish plank spreader to keep the ropes apart is good. The enemy of tree swings is water - you might like to undo the swing in winter and bring it inside the shed. Leave the eye bolt in place permanently to reduce the chance of fungal infections getting into the tree.

Not recommended to tie rope directly around the branch. Can throttle the tree’s circulation and cause the branch to drop off unexpectedlike.

Source : went through all this with my boys when they were young. Might be smart to check with council etc. to see if the method of hanging is still the recommended one.