Hang indoor swing chair BETWEEN two ceiling joists
You've hit on three viable options. I'll make some notes on each so you can decide. 

Run a cleat across the gap


Requires perhaps the most damage to the finished ceiling, but simple and fairly easy
A 2x6 laid flat against the ceiling will carry the weight just fine (avoid boards with large knots)
Four 3-1/2" by 3/8" lag screws, properly piloted into the ceiling joists, will carry well. 


Run backing in the attic


Least visible option, but most challenging due to attic work
Use a 2x4 oriented vertically (like the ceiling joists) between the trusses
Anchor with substantial lag screws and also consider laying another board across the top of everything, connecting that with lags or 3" construction screws
Locate the eye bolt carefully so you're anchored well


Span between two eye bolts with chain


Probably the simplest and quickest option, but most likely to cause issued in your drywall such as nearby screw pops since it puts the most lateral stress on the ceiling joists
To reduce lateral force which could bend or move your eye bolts (potentially shifting the ceiling joists), run your chain or cable down far enough so you have an angle less than 45 degrees to vertical, and consider using a rigid bar between the chains near the ceiling to direct force to vertical
Hang on both chains with an S-hook or proper carabiner (not a novelty item)